Relevant bibliographies by topics / Error approximation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Error approximation'

Author: Grafiati
Published: 23 September 2022
Last updated: 27 January 2023

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Journal articles on the topic "Error approximation"

1

Heltai, Luca, and Wenyu Lei. "A priori error estimates of regularized elliptic problems." Numerische Mathematik 146, no. 3 (September 29, 2020): 571–96. http://dx.doi.org/10.1007/s00211-020-01152-w.

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Abstract Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this work we show a-priori rates of convergence of this approximation process in standard Sobolev norms, with minimal regularity assumptions on the approximation of the Dirac delta distribution. The application of these estimates to the numerical solution of elliptic problems with singularly supported forcing terms allows us to provide sharp $$H^1$$ H 1 and $$L^2$$ L 2 error estimates for the corresponding regularized problem. As an application, we show how finite element approximations of a regularized immersed interface method results in the same rates of convergence of its non-regularized counterpart, provided that the support of the Dirac delta approximation is set to a multiple of the mesh size, at a fraction of the implementation complexity. Numerical experiments are provided to support our theories.
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Kato, Seiji, Fred G. Rose, and Thomas P. Charlock. "Computation of Domain-Averaged Irradiance Using Satellite-Derived Cloud Properties." Journal of Atmospheric and Oceanic Technology 22, no. 2 (February 1, 2005): 146–64. http://dx.doi.org/10.1175/jtech-1694.1.

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Abstract The respective errors caused by the gamma-weighted two-stream approximation and the effective thickness approximation for computing the domain-averaged broadband shortwave irradiance are evaluated using cloud optical thicknesses derived from 1 h of radiance measurements by the Moderate Resolution Imaging Spectrometer (MODIS) over footprints of Clouds and the Earth’s Radiant Energy System (CERES) instruments. Domains are CERES footprints of which dimension varies approximately from 20 to 70 km, depending on the viewing zenith angle of the instruments. The average error in the top-of-atmosphere irradiance at a 30° solar zenith angle caused by the gamma-weighted two-stream approximation is 6.1 W m−2 (0.005 albedo bias) with a one-layer overcast cloud where a positive value indicates an overestimate by the approximation compared with the irradiance computed using the independent column approximation. Approximately one-half of the error is due to deviations of optical thickness distributions from a gamma distribution and the other half of the error is due to other approximations in the model. The error increases to 14.7 W m−2 (0.012 albedo bias) when the computational layer dividing the cloud layer is increased to four. The increase is because of difficulties in treating the correlation of cloud properties in the vertical direction. Because the optical thickness under partly cloudy conditions, which contribute two-thirds of cloudy footprints, is smaller, the error is smaller than under overcast conditions; the average error for partly cloudy condition is −2.4 W m−2 (−0.002 albedo bias) at a 30° solar zenith angle. The corresponding average error caused by the effective thickness approximation is 0.5 W m−2 for overcast conditions and −21.5 W m−2 (−0.018 albedo bias) for partly cloudy conditions. Although the error caused by the effective thickness approximation depends strongly on the optical thickness, its average error under overcast conditions is smaller than the error caused by the gamma-weighted two-stream approximation because the errors at small and large optical thicknesses cancel each other. Based on these error analyses, the daily average error caused by the gamma-weighted two-stream and effective thickness approximations is less than 2 W m−2.
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Peköz, Erol A. "Stein's method for geometric approximation." Journal of Applied Probability 33, no. 3 (September 1996): 707–13. http://dx.doi.org/10.2307/3215352.

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The Stein–Chen method for Poisson approximation is adapted to the setting of the geometric distribution. This yields a convenient method for assessing the accuracy of the geometric approximation to the distribution of the number of failures preceding the first success in dependent trials. The results are applied to approximating waiting time distributions for patterns in coin tossing, and to approximating the distribution of the time when a stationary Markov chain first visits a rare set of states. The error bounds obtained are sharper than those obtainable using related Poisson approximations.
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Peköz, Erol A. "Stein's method for geometric approximation." Journal of Applied Probability 33, no. 03 (September 1996): 707–13. http://dx.doi.org/10.1017/s0021900200100142.

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The Stein–Chen method for Poisson approximation is adapted to the setting of the geometric distribution. This yields a convenient method for assessing the accuracy of the geometric approximation to the distribution of the number of failures preceding the first success in dependent trials. The results are applied to approximating waiting time distributions for patterns in coin tossing, and to approximating the distribution of the time when a stationary Markov chain first visits a rare set of states. The error bounds obtained are sharper than those obtainable using related Poisson approximations.
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Howard, Roy M. "Arbitrarily Accurate Analytical Approximations for the Error Function." Mathematical and Computational Applications 27, no. 1 (February 9, 2022): 14. http://dx.doi.org/10.3390/mca27010014.

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A spline-based integral approximation is utilized to define a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The real case is considered and the approximations can be improved by utilizing the approximation erf(x)≈1 for |x|>xo and with xo optimally chosen. Two generalizations are possible; the first is based on demarcating the integration interval into m equally spaced subintervals. The second, is based on utilizing a larger fixed subinterval, with a known integral, and a smaller subinterval whose integral is to be approximated. Both generalizations lead to significantly improved accuracy. Furthermore, the initial approximations, and those arising from the first generalization, can be utilized as inputs to a custom dynamic system to establish approximations with better convergence properties. Indicative results include those of a fourth-order approximation, based on four subintervals, which leads to a relative error bound of 1.43 × 10−7 over the interval [0, ∞]. The corresponding sixteenth-order approximation achieves a relative error bound of 2.01 × 10−19. Various approximations that achieve the set relative error bounds of 10−4, 10−6, 10−10, and 10−16, over [0, ∞], are specified. Applications include, first, the definition of functions that are upper and lower bounds, of arbitrary accuracy, for the error function. Second, new series for the error function. Third, new sequences of approximations for exp(−x2) that have significantly higher convergence properties than a Taylor series approximation. Fourth, the definition of a complementary demarcation function eC(x) that satisfies the constraint eC2(x)+erf2(x)=1. Fifth, arbitrarily accurate approximations for the power and harmonic distortion for a sinusoidal signal subject to an error function nonlinearity. Sixth, approximate expressions for the linear filtering of a step signal that is modeled by the error function.
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Şimşek, Burçin, and Satish Iyengar. "Approximating the Conway-Maxwell-Poisson normalizing constant." Filomat 30, no. 4 (2016): 953–60. http://dx.doi.org/10.2298/fil1604953s.

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The Conway-Maxwell-Poisson is a two-parameter family of distributions on the nonnegative integers. Its parameters ? and ? model the intensity and the dispersion, respectively. Its normalizing constant is not always easy to compute, so good approximations are needed along with an assessment of their error. Shmueli, et al. [11] derived an approximation assuming that ? is an integer, and gave an estimate of the relative error. Their numerical work showed that their approximation performs well in some parameter ranges but not in others. Our aims are to show that this approximation applies to all real ? > 0; to provide correction terms to this approximation; and to give different approximations for ? very small and very large. We then investigate the error terms numerically to assess our approximations. In parameter ranges for which Shmueli?s approximation does poorly we show that our correction terms or alternative approximations give considerable improvement.
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GREPL, MARTIN A. "CERTIFIED REDUCED BASIS METHODS FOR NONAFFINE LINEAR TIME-VARYING AND NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS." Mathematical Models and Methods in Applied Sciences 22, no. 03 (March 2012): 1150015. http://dx.doi.org/10.1142/s0218202511500151.

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We present reduced basis approximations and associated a posteriori error bounds for parabolic partial differential equations involving (i) a nonaffine dependence on the parameter and (ii ) a nonlinear dependence on the field variable. The method employs the Empirical Interpolation Method in order to construct "affine" coefficient-function approximations of the "nonaffine" (or nonlinear) parametrized functions. We consider linear time-invariant as well as linear time-varying nonaffine functions and introduce a new sampling approach to generate the function approximation space for the latter case. Our a posteriori error bounds take both error contributions explicitly into account — the error introduced by the reduced basis approximation and the error induced by the coefficient function interpolation. We show that these bounds are rigorous upper bounds for the approximation error under certain conditions on the function interpolation, thus addressing the demand for certainty of the approximation. As regards efficiency, we develop an offline–online computational procedure for the calculation of the reduced basis approximation and associated error bound. The method is thus ideally suited for the many-query or real-time contexts. Numerical results are presented to confirm and test our approach.
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GERNER, ANNA-LENA, and KAREN VEROY. "REDUCED BASISA POSTERIORIERROR BOUNDS FOR THE STOKES EQUATIONS IN PARAMETRIZED DOMAINS: A PENALTY APPROACH." Mathematical Models and Methods in Applied Sciences 21, no. 10 (October 2011): 2103–34. http://dx.doi.org/10.1142/s0218202511005672.

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We present reduced basis approximations and associated rigorous a posteriori error bounds for the Stokes equations in parametrized domains. The method, built upon the penalty formulation for saddle point problems, provides error bounds not only for the velocity but also for the pressure approximation, while simultaneously admitting affine geometric variations with relative ease. The essential ingredients are: (i) dimension reduction through Galerkin projection onto a low-dimensional reduced basis space; (ii) stable, good approximation of the pressure through supremizer-enrichment of the velocity reduced basis space; (iii) optimal and numerically stable approximations identified through an efficient greedy sampling method; (iv) certainty, through rigorous a posteriori bounds for the errors in the reduced basis approximation; and (v) efficiency, through an offline-online computational strategy. The method is applied to a flow problem in a two-dimensional channel with a (parametrized) rectangular obstacle. Numerical results show that the reduced basis approximation converges rapidly, the effectivities associated with the (inexpensive) rigorous a posteriori error bounds remain good even for reasonably small values of the penalty parameter, and that the effects of the penalty parameter are relatively benign.
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Yan, Xiaoyu, Jie Chen, Holger Nies, and Otmar Loffeld. "Analytical Approximation Model for Quadratic Phase Error Introduced by Orbit Determination Errors in Real-Time Spaceborne SAR Imaging." Remote Sensing 11, no. 14 (July 12, 2019): 1663. http://dx.doi.org/10.3390/rs11141663.

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Research on real-time spaceborne synthetic aperture radar (SAR) imaging has emerged as satellite computation capability has increased and applications of SAR imaging products have expanded. The orbit determination data of a spaceborne SAR platform are essential for the SAR imaging procedure. In real-time SAR imaging, onboard orbit determination data cannot achieve a level of accuracy that is equivalent to the orbit ephemeris in ground-based SAR processing, which requires a long processing time using common ground-based SAR imaging procedures. It is important to study the influence of errors in onboard real-time orbit determination data on SAR image quality. Instead of the widely used numerical simulation method, an analytical approximation model of the quadratic phase error (QPE) introduced by orbit determination errors is proposed. The proposed model can provide approximation results at two granularities: approximations with a satellite’s true anomaly as the independent variable and approximations for all positions in the satellite’s entire orbit. The proposed analytical approximation model reduces simulation complexity, extent of calculations, and the processing time. In addition, the model reveals the core of the process by which errors are transferred to QPE calculations. A detailed comparison between the proposed method and a numerical simulation method proves the correctness and reliability of the analytical approximation model. With the help of this analytical approximation model, the technical parameter iteration procedure during the early-stage development of an onboard real-time SAR imaging mission will likely be accelerated.
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Moon, Seonghyeon, and Kwanghee Ko. "A point projection approach for improving the accuracy of the multilevel B-spline approximation." Journal of Computational Design and Engineering 5, no. 2 (October 31, 2017): 173–79. http://dx.doi.org/10.1016/j.jcde.2017.10.004.

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Abstract In this study, we present a method for improving the accuracy of the multilevel B-spline approximation (MBA) method. We combine a point projection method with the MBA method for reducing the approximation error by directly adjusting the control points in the local area. An initial surface is generated by the MBA method, and grid points are produced on the surface. These grid points are projected onto the scattered point set, and the distances between the grid points and the projected points are computed. The control points are then modified based on the distances. The proposed method shows better approximations even with the same number of control points and ensures C2-continuity. The experimental results with examples verify the validity of the proposed method. Highlights We propose a method for improving the multilevel B-spline approximation method. We use a point projection method for computing the amount of errors. The computed errors are directly applied to the control points for reducing the approximation error.
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Dissertations / Theses on the topic "Error approximation"

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Liao, Qifeng. "Error estimation and stabilization for low order finite elements." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/error-estimation-and-stabilization-for-low-order-finite-elements(ba7fc33b-b154-404b-b608-fc8eeabd9e58).html.

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Zhang, Qi. "Multilevel adaptive radial basis function approximation using error indicators." Thesis, University of Leicester, 2016. http://hdl.handle.net/2381/38284.

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In some approximation problems, sampling from the target function can be both expensive and time-consuming. It would be convenient to have a method for indicating where the approximation quality is poor, so that generation of new data provides the user with greater accuracy where needed. In this thesis, the author describes a new adaptive algorithm for Radial Basis Function (RBF) interpolation which aims to assess the local approximation quality and adds or removes points as required to improve the error in the specified region. For a multiquadric and Gaussian approximation, one has the flexibility of a shape parameter which one can use to keep the condition number of the interpolation matrix to a moderate size. In this adaptive error indicator (AEI) method, an adaptive shape parameter is applied. Numerical results for test functions which appear in the literature are given for one, two, and three dimensions, to show that this method performs well. A turbine blade design problem form GE Power (Rugby, UK) is considered and the AEI method is applied to this problem. Moreover, a new multilevel approximation scheme is introduced in this thesis by coupling it with the adaptive error indicator. Preliminary numerical results from this Multilevel Adaptive Error Indicator (MAEI) approximation method are shown. These indicate that the MAEI is able to express the target function well. Moreover, it provides a highly efficient sampling.
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Huang, Fang-Lun. "Error analysis and tractability for multivariate integration and approximation." HKBU Institutional Repository, 2004. http://repository.hkbu.edu.hk/etd_ra/515.

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Jain, Aashish. "Error Visualization in Comparison of B-Spline Surfaces." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/35319.

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Geometric trimming of surfaces results in a new mathematical description of the matching surface. This matching surface is required to closely resemble the remaining portion of the original surface. Typically, the approximation error in such cases is measured with a view to minimize it. The data associated with the error between two matching surfaces is large and needs to be filtered into meaningful information.This research looks at suitable norms for achieving this data reduction or abstraction with a view to provide quantitative feedback about the approximation error. Also, the differences between geometric shapes are easily discerned by the human eye but are difficult to characterize or describe. Error visualization tools have been developed to provide effective visual inputs that the designer can interpret into meaningful information.
Master of Science
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Dziegielewski, Andreas von [Verfasser]. "High precision swept volume approximation with conservative error bounds / Andreas von Dziegielewski." Mainz : Universitätsbibliothek Mainz, 2012. http://d-nb.info/1029217343/34.

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Grepl, Martin A. (Martin Alexander) 1974. "Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/32387.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.
Includes bibliographical references (p. 243-251).
Modern engineering problems often require accurate, reliable, and efficient evaluation of quantities of interest, evaluation of which demands the solution of a partial differential equation. We present in this thesis a technique for the prediction of outputs of interest of parabolic partial differential equations. The essential ingredients are: (i) rapidly convergent reduced-basis approximations - Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter-time space; (ii) a posteriori error estimation - relaxations of the error-residual equation that provide rigorous and sharp bounds for the error in specific outputs of interest: the error estimates serve a priori to construct our samples and a posteriori to confirm fidelity; and (iii) offline-online computional procedures - in the offline stage the reduced- basis approximation is generated; in the online stage, given a new parameter value, we calculate the reduced-basis output and associated error bound. The operation count for the online stage depends only on N (typically small) and the parametric complexity of the problem; the method is thus ideally suited for repeated, rapid, reliable evaluation of input-output relationships in the many-query or real-time contexts. We first consider parabolic problems with affine parameter dependence and subsequently extend these results to nonaffine and certain classes of nonlinear parabolic problems.
(cont.) To this end, we introduce a collateral reduced-basis expansion for the nonaffine and nonlinear terms and employ an inexpensive interpolation procedure to calculate the coefficients for the function approximation - the approach permits an efficient offline-online computational decomposition even in the presence of nonaffine and highly nonlinear terms. Under certain restrictions on the function approximation, we also introduce rigorous a posteriori error estimators for nonaffine and nonlinear problems. Finally, we apply our methods to the solution of inverse and optimal control problems. While the efficient evaluation of the input-output relationship is essential for the real-time solution of these problems, the a posteriori error bounds let us pursue a robust parameter estimation procedure which takes into account the uncertainty due to measurement and reduced-basis modeling errors explicitly (and rigorously). We consider several examples: the nondestructive evaluation of delamination in fiber-reinforced concrete, the dispersion of pollutants in a rectangular domain, the self-ignition of a coal stockpile, and the control of welding quality. Numerical results illustrate the applicability of our methods in the many-query contexts of optimization, characterization, and control.
by Martin A. Grepl.
Ph.D.
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White, Staci A. "Quantifying Model Error in Bayesian Parameter Estimation." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1433771825.

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Parker, William David. "Speeding Up and Quantifying Approximation Error in Continuum Quantum Monte Carlo Solid-State Calculations." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1284495775.

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Vail, Michelle Louise. "Error estimates for spaces arising from approximation by translates of a basic function." Thesis, University of Leicester, 2002. http://hdl.handle.net/2381/30519.

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We look at aspects of error analysis for interpolation by translates of a basic function. In particular, we consider ideas of localisation and how they can be used to obtain improved error estimates. We shall consider certain seminorms and associated spaces of functions which arise in the study of such interpolation methods. These seminorms are naturally given in an indirect form, that is in terms of the Fourier Transform of the function rather than the function itself. Thus, they do not lend themselves to localisation. However, work by Levesley and Light [17] rewrites these seminorms in a direct form and thus gives a natural way of defining a local seminorm. Using this form of local seminorm we construct associated local spaces. We develop bounded, linear extension operators for these spaces and demonstrate how such extension operators can be used in developing improved error estimates. Specifically, we obtain improved L2 estimates for these spaces in terms of the spacing of the interpolation points. Finally, we begin a discussion of how this approach to localisation compares with alternatives.
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Rankin, Richard Andrew Robert. "Fully computable a posteriori error bounds for noncomforming and discontinuous galekin finite elemant approximation." Thesis, University of Strathclyde, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.501776.

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We obtain fully computable constant free a posteriori error bounds on the broken energy seminorm of the error in nonconforming and discontinuous Galerkin finite element approximations of a linear second ore elliptic problem on meshes omprised of triangular elements. We do this for nonconforming finite element approximations of uniform arbitrary order as well as for non-uniform order symmetric interior penalty Galerkin, non-symmetric interior penalty Galerkin and ncomplete interior penalty Galerkin finite element approximations.
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Books on the topic "Error approximation"

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Agarwal, Ravi P. Error inequalities in polynomial interpolation and their applications. Dordrecht, Netherlands: Kluwer Academic Publishers, 1993.

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P, Dobrovolʹskiĭ I., ed. Ob ot͡s︡enke pogreshnosteĭ pri ėkstrapoli͡a︡t͡s︡ii Richardsona. Moskva: Vychislitelʹnyĭ t͡s︡entr AN SSSR, 1987.

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Maday, Yvon. Error analysis for spectral approximation of the Korteweg-de Vries equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1987.

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Michael, Evans. An algorithm for the approximation of integrals with exact error bounds. Toronto: University of Toronto, Dept. of Statistics, 1997.

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Maday, Yvon. A well-posed optimal spectral element approximation for the Stokes problem. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1987.

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Maday, Yvon. A well-posed optimal spectral element approximation for the Stokes problem. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1987.

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Maday, Yvon. A well-posed optimal spectral element approximation for the Stokes problem. Hampton, Va: ICASE, 1987.

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Novak, Erich. Deterministic and stochastic error bounds in numerical analysis. Berlin: Springer-Verlag, 1988.

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Lakshmikantham, V. Computational error and complexity in science and engineering. Boston: Elsevier, 2005.

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I, Repin Sergey, ed. Reliable methods for computer simulation: Error control and a posteriori estimates. Amsterdam: Elsevier, 2004.

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Book chapters on the topic "Error approximation"

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Deutsch, Frank. "Error of Approximation." In Best Approximation in Inner Product Spaces, 125–53. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4684-9298-9_7.

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de Villiers, Johan. "Error Analysis for Polynomial Interpolation." In Mathematics of Approximation, 25–35. Paris: Atlantis Press, 2012. http://dx.doi.org/10.2991/978-94-91216-50-3_2.

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Hromadka, Theodore V., and Chintu Lai. "Reducing CVBEM Approximation Error." In The Complex Variable Boundary Element Method in Engineering Analysis, 210–52. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-4660-2_6.

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Brezinski, Claude. "Error estimate in pade approximation." In Orthogonal Polynomials and their Applications, 1–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0083350.

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Brezinski, C. "Error Estimates in Padé Approximation." In Error Control and Adaptivity in Scientific Computing, 75–85. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4647-0_4.

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Waldvogel, Jörg. "Towards a General Error Theory of the Trapezoidal Rule." In Approximation and Computation, 267–82. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6594-3_17.

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Luik, Eberhard. "Cubature Error Bounds using Degrees of Approximation." In Multivariate Approximation Theory III, 286–97. Basel: Birkhäuser Basel, 1985. http://dx.doi.org/10.1007/978-3-0348-9321-3_28.

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Mukhopadhyay, Jayanta. "Error Analysis: Analytical Approaches." In Approximation of Euclidean Metric by Digital Distances, 39–56. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-9901-9_3.

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Mukhopadhyay, Jayanta. "Error Analysis: Geometric Approaches." In Approximation of Euclidean Metric by Digital Distances, 57–102. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-9901-9_4.

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Brass, H. "Error Bounds Based on Approximation Theory." In Numerical Integration, 147–63. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2646-5_12.

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Conference papers on the topic "Error approximation"

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Yamazaki, Keisuke. "Generative approximation of generalization error." In 2009 IEEE International Workshop on Machine Learning for Signal Processing (MLSP). IEEE, 2009. http://dx.doi.org/10.1109/mlsp.2009.5306243.

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Tarvainen, Tanja, Ville Kolehmainen, Aki Pulkkinen, Marko Vauhkonen, Martin Schweiger, Simon R. Arridge, and Jari P. Kaipio. "Approximation Error Approach for Compensating Modelling Errors in Optical Tomography." In Biomedical Optics. Washington, D.C.: OSA, 2010. http://dx.doi.org/10.1364/biomed.2010.bsud48.

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Hu, Guangyan, Sandro Rigo, Desheng Zhang, and Thu Nguyen. "Approximation with Error Bounds in Spark." In 2019 IEEE 27th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS). IEEE, 2019. http://dx.doi.org/10.1109/mascots.2019.00017.

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Stolpner, Svetlana, and Sue Whitesides. "Medial Axis Approximation with Bounded Error." In 2009 Sixth International Symposium on Voronoi Diagrams (ISVD). IEEE, 2009. http://dx.doi.org/10.1109/isvd.2009.24.

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Kalvin, Alan D., and Russell H. Taylor. "Superfaces: polyhedral approximation with bounded error." In Medical Imaging 1994, edited by Yongmin Kim. SPIE, 1994. http://dx.doi.org/10.1117/12.173991.

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Kharinov, Mikhail Vyacheslavovich. "Example-Based Object Detection in the Attached Image." In 32nd International Conference on Computer Graphics and Vision. Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/graphicon-2022-490-501.

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The paper solves the problem of detecting exemplified objects in a color image. A solution provides the representation of similar objects in the same colors, and different objects in different colors. This is achieved by combining images of object examples and a target image into a single joint image, which is represented in sequential number 1, 2, ..., etc. colors. The mentioned effect is demonstrated by detecting irises and pupils in a test image. It is explained by the fact that: a) the joint image is approximated by a hierarchy of approximations in sequential color numbers; b) the hierarchy of approximations is described by a convex sequence of approximation errors (values of the total squared error ); c) due to the convexity, the approximation errors are reduced for all approximations of the joint image. In the last explanation item, it is applied the operation of combining hierarchically organized objects into a single object, which is introduced in this paper. To produce the required hierarchy of image approximations Ward's pixel clustering is used. Ward's method is generalized for image processing by parts (within pixel subsets) that provides generation of multiple proper approximation hierarchies and accelerates the calculations. To do so, the so- called split-and-merge pixel cluster CI-method is embedded into Ward's generalized method to provide a real-life minimization of the error for image approximation in a fixed number of colors.
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Ye, Peixin. "Quantum Approximation Error on Some Sobolev Classes." In Third International Conference on Natural Computation (ICNC 2007). IEEE, 2007. http://dx.doi.org/10.1109/icnc.2007.588.

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Koponen, Janne, Tomi Huttunen, Tanja Tarvainen, and Jari Kaipio. "Approximation error method for full-wave tomography." In ICA 2013 Montreal. ASA, 2013. http://dx.doi.org/10.1121/1.4800022.

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Nguyen, Dzung T., Minh D. Dao, and Trac D. Tran. "Error concealment via 3-mode tensor approximation." In 2011 18th IEEE International Conference on Image Processing (ICIP 2011). IEEE, 2011. http://dx.doi.org/10.1109/icip.2011.6115891.

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Shintani, Eigo. "Error reduction using the covariant approximation averaging." In The European Physical Society Conference on High Energy Physics. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.234.0367.

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Reports on the topic "Error approximation"

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Hesthaven, Jan S., and Anthony T. Patera. Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 2010. http://dx.doi.org/10.21236/ada563403.

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Urban, Karsten, and Anthony T. Patera. A New Error Bound for Reduced Basis Approximation of Parabolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, January 2012. http://dx.doi.org/10.21236/ada557547.

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Arhin, Stephen, Babin Manandhar, Kevin Obike, and Melissa Anderson. Impact of Dedicated Bus Lanes on Intersection Operations and Travel Time Model Development. Mineta Transportation Institute, June 2022. http://dx.doi.org/10.31979/mti.2022.2040.

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Over the years, public transit agencies have been trying to improve their operations by continuously evaluating best practices to better serve patrons. Washington Metropolitan Area Transit Authority (WMATA) oversees the transit bus operations in the Washington Metropolitan Area (District of Columbia, some parts of Maryland and Virginia). One practice attempted by WMATA to improve bus travel time and transit reliability has been the implementation of designated bus lanes (DBLs). The District Department of Transportation (DDOT) implemented a bus priority program on selected corridors in the District of Columbia leading to the installation of red-painted DBLs on corridors of H Street, NW, and I Street, NW. This study evaluates the impacts on the performance of transit buses along with the general traffic performance at intersections on corridors with DBLs installed in Washington, DC by using a “before” and “after” approach. The team utilized non-intrusive video data to perform vehicular turning movement counts to assess the traffic flow and delays (measures of effectiveness) with a traffic simulation software. Furthermore, the team analyzed the Automatic Vehicle Locator (AVL) data provided by WMATA for buses operating on the study segments to evaluate bus travel time. The statistical analysis showed that the vehicles traveling on H Street and I Street (NW) experienced significantly lower delays during both AM (7:00–9:30 AM) and PM (4:00–6:30 PM) peak hours after the installation of bus lanes. The approximation error metrics (normalized squared errors) for the testing dataset was 0.97, indicating that the model was predicting bus travel times based on unknown data with great accuracy. WMATA can apply this research to other segments with busy bus schedules and multiple routes to evaluate the need for DBLs. Neural network models can also be used to approximate bus travel times on segments by simulating scenarios with DBLs to obtain accurate bus travel times. Such implementation could not only improve WMATA’s bus service and reliability but also alleviate general traffic delays.
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Cogan, James. Some Potential Errors in Satellite Wind Estimates Using the Geostrophic Approximation and the Thermal Wind. Fort Belvoir, VA: Defense Technical Information Center, June 1993. http://dx.doi.org/10.21236/ada269784.

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Mokole, Eric L. Contributions to Radar Tracking Errors for a Two-Point Target Caused by Geometric Approximations. Fort Belvoir, VA: Defense Technical Information Center, September 1991. http://dx.doi.org/10.21236/ada241635.

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Girolamo Neto, Cesare, Rodolfo Jaffe, Rosane Cavalcante, and Samia Nunes. Comparacao de modelos para predicao do desmatamento na Amazonia brasileira. ITV, 2021. http://dx.doi.org/10.29223/prod.tec.itv.ds.2021.25.girolamoneto.

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O presente relatório contém resultados parciais do projeto “Definição de áreas prioritárias para recuperação florestal”, referentes a atividade “Uso e comparação da acurácia de diferentes modelos preditivos de desmatamento na Amazônia”. O objetivo deste estudo foi a implementação de modelos preditivos de desmatamento na Amazônia brasileira com base nas técnicas de Random Forest (RF), Spatial Random Forest (SpRF) e Integrated Nested Laplace Approximations (INLA) e comparação dos erros obtidos com cada modelo. Uma base de dados geográficos foi gerada por meio da integração de dados de diversas instituições brasileiras, como IBGE, MMA e INPE, utilizando células de 25 x 25 km e uma janela temporal de um ano. Os principais drivers de desmatamento identificados estão relacionados à fragmentação florestal e à expansão de áreas de pastagem na Amazônia, corroborando com outros trabalhos encontrados em literatura. A modelagem obteve melhores resultados com o uso dos modelos RF e SpRF em relação aos modelos do tipo INLA, com menores valores de erro médio quadrático obtido em conjuntos de dados de treinamento e validação dos algoritmos. A previsão de desmatamento para o ano de 2020 foi de 31 mil km2 , dados que apresentam uma superestimava devido ao método utilizado para o cálculo do desmatamento. Entre as ações identificadas que podem ser adotadas em trabalhos futuros para melhorar a previsão do desmatamento, cita-se o uso da abordagem CLUE e a melhoria de algumas bases de dados utilizada, a exemplo da malha viária.
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Kamai, Tamir, Gerard Kluitenberg, and Alon Ben-Gal. Development of heat-pulse sensors for measuring fluxes of water and solutes under the root zone. United States Department of Agriculture, January 2016. http://dx.doi.org/10.32747/2016.7604288.bard.

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The objectives defined for this study were to: (1) develop a heat-pulse sensor and a heat-transfer model for leaching measurement, and (2) conduct laboratory study of the sensor and the methodology to estimate leaching flux. In this study we investigated the feasibility for estimating leachate fluxes with a newly designed heat-pulse (HP) sensor, combining water flux density (WFD) with electrical conductivity (EC) measurements in the same sensor. Whereas previous studies used the conventional heat pulse sensor for these measurements, the focus here was to estimate WFD with a robust sensor, appropriate for field settings, having thick-walled large-diameter probes that would minimize their flexing during and after installation and reduce associated errors. The HP method for measuring WFD in one dimension is based on a three-rod arrangement, aligned in the direction of the flow (vertical for leaching). A heat pulse is released from a center rod and the temperature response is monitored with upstream (US) and downstream (DS) rods. Water moving through the soil caries heat with it, causing differences in temperature response at the US and DS locations. Appropriate theory (e.g., Ren et al., 2000) is then used to determine WFD from the differences in temperature response. In this study, we have constructed sensors with large probes and developed numerical and analytical solutions for approximating the measurement. One-dimensional flow experiments were conducted with WFD ranging between 50 and 700 cm per day. A numerical model was developed to mimic the measurements, and also served for the evaluation of the analytical solution. For estimation WFD, and analytical model was developed to approximate heat transfer in this setting. The analytical solution was based on the work of Knight et al. (2012) and Knight et al. (2016), which suggests that the finite properties of the rods can be captured to a large extent by assuming them to be cylindrical perfect conductors. We found that: (1) the sensor is sensitive for measuring WFD in the investigated range, (2) the numerical model well-represents the sensor measurement, and (2) the analytical approximation could be improved by accounting for water and heat flow divergence by the large rods.
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Hart, Carl, and Gregory Lyons. A tutorial on the rapid distortion theory model for unidirectional, plane shearing of homogeneous turbulence. Engineer Research and Development Center (U.S.), July 2022. http://dx.doi.org/10.21079/11681/44766.

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The theory of near-surface atmospheric wind noise is largely predicated on assuming turbulence is homogeneous and isotropic. For high turbulent wavenumbers, this is a fairly reasonable approximation, though it can introduce non-negligible errors in shear flows. Recent near-surface measurements of atmospheric turbulence suggest that anisotropic turbulence can be adequately modeled by rapid-distortion theory (RDT), which can serve as a natural extension of wind noise theory. Here, a solution for the RDT equations of unidirectional plane shearing of homogeneous turbulence is reproduced. It is assumed that the time-varying velocity spectral tensor can be made stationary by substituting an eddy-lifetime parameter in place of time. General and particular RDT evolution equations for stochastic increments are derived in detail. Analytical solutions for the RDT evolution equation, with and without an effective eddy viscosity, are given. An alternative expression for the eddy-lifetime parameter is shown. The turbulence kinetic energy budget is examined for RDT. Predictions by RDT are shown for velocity (co)variances, one-dimensional streamwise spectra, length scales, and the second invariant of the anisotropy tensor of the moments of velocity. The RDT prediction of the second invariant for the velocity anisotropy tensor is shown to agree better with direct numerical simulations than previously reported.
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Arhin, Stephen, Babin Manandhar, Hamdiat Baba Adam, and Adam Gatiba. Predicting Bus Travel Times in Washington, DC Using Artificial Neural Networks (ANNs). Mineta Transportation Institute, April 2021. http://dx.doi.org/10.31979/mti.2021.1943.

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Washington, DC is ranked second among cities in terms of highest public transit commuters in the United States, with approximately 9% of the working population using the Washington Metropolitan Area Transit Authority (WMATA) Metrobuses to commute. Deducing accurate travel times of these metrobuses is an important task for transit authorities to provide reliable service to its patrons. This study, using Artificial Neural Networks (ANN), developed prediction models for transit buses to assist decision-makers to improve service quality and patronage. For this study, we used six months of Automatic Vehicle Location (AVL) and Automatic Passenger Counting (APC) data for six Washington Metropolitan Area Transit Authority (WMATA) bus routes operating in Washington, DC. We developed regression models and Artificial Neural Network (ANN) models for predicting travel times of buses for different peak periods (AM, Mid-Day and PM). Our analysis included variables such as number of served bus stops, length of route between bus stops, average number of passengers in the bus, average dwell time of buses, and number of intersections between bus stops. We obtained ANN models for travel times by using approximation technique incorporating two separate algorithms: Quasi-Newton and Levenberg-Marquardt. The training strategy for neural network models involved feed forward and errorback processes that minimized the generated errors. We also evaluated the models with a Comparison of the Normalized Squared Errors (NSE). From the results, we observed that the travel times of buses and the dwell times at bus stops generally increased over time of the day. We gathered travel time equations for buses for the AM, Mid-Day and PM Peaks. The lowest NSE for the AM, Mid-Day and PM Peak periods corresponded to training processes using Quasi-Newton algorithm, which had 3, 2 and 5 perceptron layers, respectively. These prediction models could be adapted by transit agencies to provide the patrons with accurate travel time information at bus stops or online.
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Governing equations and model approximation errors associated with the effects of fluid-storage transients on solute transport in aquifers. US Geological Survey, 1990. http://dx.doi.org/10.3133/wri904156.

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