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Books on the topic 'Error approximation'

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Published: 23 September 2022
Last updated: 27 January 2023

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1

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

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2

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

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3

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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4

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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5

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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6

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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7

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

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8

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

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9

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

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10

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

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11

Wang, Chʻing-lin. A numerical procedure for recovering true scattering coefficients from measurements with wide-beam antennas. Lawrence, Kan: Unversity of Kansas Center for Research, Inc., Radar Systems and Remote Sensing Laboratory, 1991.

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12

Diskin, Boris. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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13

Funaro, Daniele. Convergence results for pseudospectral approximations of hyperbolic systems by a penalty type boundary treatment. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1989.

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14

Funaro, Daniele. Convergence results for pseudospectral approximations of hyperbolic systems by a penalty type boundary treatment. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1989.

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15

Diskin, Boris. New factorizable discretizations for the Euler equations. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.

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16

Diskin, Boris. Analysis of boundary conditions for factorizable discretizations of the Euler equations. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.

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17

Kemp, Gordon C. R. Approximating the joint distribution of one-step ahead forecast errors in the AR(1) model. [Colchester]: University of Essex, Dept. of Economics, 1988.

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18

Goode, Daniel J. Governing equations and model approximation errors associated with the effects of fluid-storage transients on solute transport in aquifers. Reston, Va: U.S. Dept. of the Interior, U.S. Geological Survey, 1990.

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19

Geometry and codes. Dordrecht [Netherlands]: Kluwer Academic Publishers, 1988.

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20

Gregory, R. T., and E. V. Krishnamurthy. Methods and Applications of Error-Free Computation. Springer, 2012.

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21

Gregory, R. T. Methods and Applications of Error-Free Computation. Springer, 2011.

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22

Howell, Gary Wilbur. Error bounds for polynomial and spline interpolation. 1986.

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23

Neittaanmäki, Pekka, and Sergey R. Repin. Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates. Elsevier Science & Technology Books, 2004.

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24

J, Vanderaar Mark, and United States. National Aeronautics and Space Administration., eds. A planar approximation for the least reliable bit log-likelihood ratio of 8-PSK modulation. [Washington, D.C.]: National Aeronautics and Space Administration, 1994.

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25

J, Vanderaar Mark, and United States. National Aeronautics and Space Administration., eds. A planar approximation for the least reliable bit log-likelihood ratio of 8-PSK modulation. [Washington, D.C.]: National Aeronautics and Space Administration, 1994.

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26

Deterministic and Stochastic Error Bounds in Numerical Analysis Lecture Notes in Mathematics. Springer, 1988.

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27

Institute for Computer Applications in Science and Engineering., ed. Minimization of the truncation error by grid adaptation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1999.

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28

Neittaanmäki, Pekka, and Sergey Repin. Reliable Methods for Computer Simulation, Volume 33: Error Control and Posteriori Estimates (Studies in Mathematics and its Applications). Elsevier Science, 2004.

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29

Center, Langley Research, ed. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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30

Center, Langley Research, ed. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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31

Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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32

Center, Langley Research, ed. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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33

United States. National Aeronautics and Space Administration, ed. Error assessments of widely-used orbit error approximations in satellite altimetry. [Washington, DC: National Aeronautics and Space Administration, 1988.

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34

Gershman, Samuel. What Makes Us Smart. Princeton University Press, 2021. http://dx.doi.org/10.23943/princeton/9780691205717.001.0001.

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At the heart of human intelligence rests a fundamental puzzle: How are we incredibly smart and stupid at the same time? No existing machine can match the power and flexibility of human perception, language, and reasoning. Yet, we routinely commit errors that reveal the failures of our thought processes. This book makes sense of this paradox by arguing that our cognitive errors are not haphazard. Rather, they are the inevitable consequences of a brain optimized for efficient inference and decision making within the constraints of time, energy, and memory—in other words, data and resource limitations. Framing human intelligence in terms of these constraints, the book shows how a deeper computational logic underpins the “stupid” errors of human cognition. Embarking on a journey across psychology, neuroscience, computer science, linguistics, and economics, the book presents unifying principles that govern human intelligence. First, inductive bias: any system that makes inferences based on limited data must constrain its hypotheses in some way before observing data. Second, approximation bias: any system that makes inferences and decisions with limited resources must make approximations. Applying these principles to a range of computational errors made by humans, the book demonstrates that intelligent systems designed to meet these constraints yield characteristically human errors. Examining how humans make intelligent and maladaptive decisions, the book delves into the successes and failures of cognition.
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35

Fox, Raymond. The Use of Self. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780190616144.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.
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36

Raff, Lionel, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam. Neural Networks in Chemical Reaction Dynamics. Oxford University Press, 2012. http://dx.doi.org/10.1093/oso/9780199765652.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.
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37

Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations. Springer London, Limited, 2006.

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38

A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations (Advances in Mechanics and Mathematics). Springer, 2004.

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39

Walsh, Bruce, and Michael Lynch. Theorems of Natural Selection: Results of Price, Fisher, and Robertson. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198830870.003.0006.

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This chapter reviews a number of “theorems” of natural selection. These include exact results (true mathematical theorems): the Robertson-Price identity, Price's general expression for any form of selection response, and the Fisher-Price-Ewens version of Fisher's fundamental theorem. Their generality comes as the cost of usually being very difficult to apply. An important exception is the Robertson-Price identity, which expresses the within-generation change in the mean of a trait as its covariance with relative fitness. This chapter also examines three classic approximations: Fisher's fundamental theorem for the behavior of mean population fitness, and Robertson's secondary theorem and the breeder's equation for the expected response in a trait under selection, showing both how these results are connected and the error given by the various approximations. Finally, the chapter examines the connection between the additive variance of a trait and its correlation with fitness.
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40

Lambert A.M.* Assamoi. A finite element approach wherein the errors of approximation are confined to the constitutive equations. 1987.

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41

Boudreau, Joseph F., and Eric S. Swanson. Continuum dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0019.

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The theory and application of a variety of methods to solve partial differential equations are introduced in this chapter. These methods rely on representing continuous quantities with discrete approximations. The resulting finite difference equations are solved using algorithms that stress different traits, such as stability or accuracy. The Crank-Nicolson method is described and extended to multidimensional partial differential equations via the technique of operator splitting. An application to the time-dependent Schrödinger equation, via scattering from a barrier, follows. Methods for solving boundary value problems are explored next. One of these is the ubiquitous fast Fourier transform which permits the accurate solution of problems with simple boundary conditions. Lastly, the finite element method that is central to modern engineering is developed. Methods for generating finite element meshes and estimating errors are also discussed.
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42

Okecha, George Emese. Numerical quadrature involving singular and non-singular integrals: Methods, based on Gaussian and other quadrature formulae, involving complex integration, for numerical approximation of some singular and non-singular integrals, with estimates or bounds for errors incurred. Bradford, 1985.

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