Journal articles: 'Constrained mock-Chebyshev least squares'

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De Marchi, S., F. Dell’Accio, and M. Mazza. "On the constrained mock-Chebyshev least-squares." Journal of Computational and Applied Mathematics 280 (May 2015): 94–109. http://dx.doi.org/10.1016/j.cam.2014.11.032.

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Dell’Accio, Francesco, Domenico Mezzanotte, Federico Nudo, and Donatella Occorsio. "Numerical approximation of Fredholm integral equation by the constrained mock-Chebyshev least squares operator." Journal of Computational and Applied Mathematics 447 (September 2024): 115886. http://dx.doi.org/10.1016/j.cam.2024.115886.

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Dell’Accio, Francesco, Filomena Di Tommaso, and Federico Nudo. "Generalizations of the constrained mock-Chebyshev least squares in two variables: Tensor product vs total degree polynomial interpolation." Applied Mathematics Letters 125 (March 2022): 107732. http://dx.doi.org/10.1016/j.aml.2021.107732.

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Parnovsky, S. L. "Bias of the Hubble Constant Value Caused by Errors in Galactic Distance Indicators." Ukrainian Journal of Physics 66, no. 11 (November 30, 2021): 955. http://dx.doi.org/10.15407/ujpe66.11.955.

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The bias in the determination of the Hubble parameter and the Hubble constant in the modern Universe is discussed. It could appear due to the statistical processing of data on the redshifts of galaxies and the estimated distances based on some statistical relations with limited accuracy. This causes a number of effects leading to either underestimation or overestimation of the Hubble parameter when using any methods of statistical processing, primarily the least squares method (LSM). The value of the Hubble constant is underestimated when processing a whole sample; when the sample is constrained by distance, especially when constrained from above. Moreover, it is significantly overestimated due to the data selection. The bias significantly exceeds the values of the erro ofr the Hubble constant calculated by the LSM formulae. These effects are demonstrated both analytically and using Monte Carlo simulations, which introduce deviations in the velocities and estimated distances to the original dataset described by the Hubble law. The characteristics of the deviations are similar to real observations. Errors in the estimated distances are up to 20%. They lead to the fact that, when processing the same mock sample using LSM, it is possible to obtain an estimate of the Hubble constant from 96% of the true value when processing the entire sample to 110% when processing the subsample with distances limited from above. The impact of these effects can lead to a bias in the Hubble constant obtained from real data and an overestimation of the accuracy of determining this value. This may call into question the accuracy of determining the Hubble constant and can significantly reduce the tension between the values obtained from the observations in the early and modern Universes, which were actively discussed during the last year.

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Economou, D., C. Mavroidis, I. Antoniadis, and C. Lee. "Maximally Robust Input Preconditioning for Residual Vibration Suppression Using Low-Pass FIR Digital Filters." Journal of Dynamic Systems, Measurement, and Control 124, no. 1 (July 27, 2000): 85–97. http://dx.doi.org/10.1115/1.1434272.

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A method for suppressing residual vibrations in flexible systems is presented and experimentally demonstrated. The proposed method is based on the preconditioning of the inputs to the system using low-pass Finite Impulse Response (FIR) digital filters. Provided that the cutoff frequency of FIR filters is selected lower than the lowest expected natural frequency of the system and their stop-band is maximized, we show that these filters can be designed to exhibit maximally robust behavior with respect to changes of the system natural frequencies. To perform the proper design of FIR filters for robust vibration suppression, this paper introduces a series of dimensionless performance indexes and the Delay-Error-Order (DEO) curves that represent graphically the delay time introduced by the filter as a function of the remaining residual vibrations, and the filter order. Several classes of FIR filters such as: a) Parks-McClellan; b) Window-based methods (using Chebyshev window); and c) Constrained Least Squares method, are shown to present maximally robust behavior, almost identical to the theoretically predicted. Parallel, they demonstrate excellent vibration suppression while they introduce the minimum possible delay. Further advantages offered by the proposed method, is that no modeling of the flexible system is required, the method can be used in a variety of systems exhibiting vibrations, it is independent of the guidance function and it is simple to implement in practical applications. The results are experimentally verified on a flexible aluminum beam with a significantly varying mass, attached to the end-effector of a robot manipulator. The beam is rotated, using one joint of the manipulator, from an initial to a final position. It is shown that the preconditioned inputs to the flexible system induce very little amount of residual vibrations compared to the inputs with no preconditioning.

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TANG, Jingyuan, Yongjie GOU, Yangyang MA, and Binfeng PAN. "Rocket landing guidance based on second-order Picard-Chebyshev-Newton type algorithm." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 42, no. 1 (February 2024): 98–107. http://dx.doi.org/10.1051/jnwpu/20244210098.

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This paper proposes a rocket substage vertical landing guidance method based on the second-order Picard-Chebyshev-Newton type algorithm. Firstly, the continuous-time dynamic equation is discretized based on the natural second-order Picard iteration formulation and the Chebyshev polynomial. Secondly, the landing problem that considers terminal constraints is transformed into a nonlinear least-squares problem with respect to the terminal constraint function and solved with the Gauss-Newton method. In addition, the projection method is introduced to the iteration process of the Gauss-Newton method to realize the inequality constraints of the thrust. Finally, the closed-loop strategy for rocket substage vertical landing guidance is proposed and the numerical simulations of the rocket vertical landing stage are carried out. The simulation results demonstrate that compared with the sequential convex optimization algorithm, the proposed algorithm has higher computational efficiency.

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Boyd, John P., and Fei Xu. "Divergence (Runge Phenomenon) for least-squares polynomial approximation on an equispaced grid and Mock–Chebyshev subset interpolation." Applied Mathematics and Computation 210, no. 1 (April 2009): 158–68. http://dx.doi.org/10.1016/j.amc.2008.12.087.

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Wang, Xianghui, Mei Li, Yingke Zhao, Jiao Wang, and Xin Tan. "Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level." Sensors 23, no. 7 (April 4, 2023): 3733. http://dx.doi.org/10.3390/s23073733.

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The differential microphone array, or differential beamformer, has attracted much attention for its frequency-invariant beampattern, high directivity factor and compact size. In this work, the design of differential beamformers with small inter-element spacing planar microphone arrays is concerned. In order to exactly control the main lobe beamwidth and sidelobe level and obtain minimum main lobe beamwidth with a given sidelobe level, we design the desired beampattern by applying the Chebyshev polynomials at first, via exploiting the structure of the frequency-independent beampattern of a theoretical Nth-order differential beamformer. Next, the so-called null constrained and least square beamformers, which can obtain approximately frequency-invariant beampattern at relatively low frequencies and can be steered to any direction without beampattern distortion, are proposed based on planar microphone arrays to approximate the designed desired beampatterns. Then, for dealing with the white noise amplification at low-frequency bands and beampattern divergence problems at high-frequency bands of the null constrained and least square beamformers, the so-called minimum norm and combined solutions are deduced, which can compromise among the white noise gain, directivity factor and beampattern distortion flexibly. Preliminary simulation results illustrate the properties and advantages of the proposed differential beamformers.

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Kosari, Amirreza, Hossein Maghsoudi, and Abolfazl Lavaei. "Path generation for flying robots in mountainous regions." International Journal of Micro Air Vehicles 9, no. 1 (December 23, 2016): 44–60. http://dx.doi.org/10.1177/1756829316678877.

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In this paper, a new path planning method is proposed to resolve the problem of two-dimensional terrain following flight of flying robots in mountainous regions. The performance criteria considered for this mission design could include either the minimum vertical acceleration or the minimum flying time. To impose the terrain following/terrain avoidance constraints, various approaches such as least square method, Fourier series method, Gaussian estimation method, and Chebyshev orthogonal polynomial are explored. The resulting optimal control problem is discretized by employing a numerical technique namely direct collocation and then transformed into a nonlinear programming problem. The efficacy of the proposed method is demonstrated by extensive simulations, and particularly, it has been verified that this method is able to produce a solution that satisfies all hard constraints of the underlying problem.

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Baigunchekov, Zhumadil, Med Amine Laribi, Giuseppe Carbone, Azamat Mustafa, Bekzat Amanov, and Yernar Zholdassov. "Structural-Parametric Synthesis of the RoboMech Class Parallel Mechanism with Two Sliders." Applied Sciences 11, no. 21 (October 21, 2021): 9831. http://dx.doi.org/10.3390/app11219831.

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This paper addresses the structural-parametric synthesis and kinematic analysis of the RoboMech class of parallel mechanisms (PM) having two sliders. The proposed methods allow the synthesis of a PM with its structure and geometric parameters of the links to obtain the given laws of motions of the input and output links (sliders). The paper outlines a possible application of the proposed approach to design a PM for a cold stamping technological line. The proposed PM is formed by connecting two sliders (input and output objects) using one passive and one negative closing kinematic chain (CKC). The passive CKC does not impose a geometric constraint on the movements of the sliders and the geometric parameters of its links are varied to satisfy the geometric constraint of the negative CKC. The negative CKC imposes one geometric constraint on the movements of the sliders and its geometric parameters are determined on the basis of the Chebyshev and least-square approximations. Problems of positions and analogues of velocities and accelerations of the considered PM are solved to demonstrate the feasibility and effectiveness of the proposed formulations and case of study.

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Baigunchekov, Zhumadil, Med Amine Laribi, Azamat Mustafa, and Abzal Kassinov. "Kinematic Synthesis and Analysis of the RoboMech Class Parallel Manipulator with Two Grippers." Robotics 10, no. 3 (August 3, 2021): 99. http://dx.doi.org/10.3390/robotics10030099.

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In this paper, methods of kinematic synthesis and analysis of the RoboMech class parallel manipulator (PM) with two grippers (end effectors) are presented. This PM is formed by connecting two output objects (grippers) with a base using two passive and one negative closing kinematic chains (CKCs). A PM with two end effectors can be used for reloading operations of stamped products between two adjacent main technologies in a cold stamping line. Passive CKCs represent two serial manipulators with two degrees of freedom, and negative CKC is a three-joined link with three negative degrees of freedom. A negative CKC imposes three geometric constraints on the movements of the two output objects. Geometric parameters of the negative CKC are determined on the basis of the problems of the Chebyshev and least-square approximations. Problems of positions and analogues of velocities and accelerations of the PM with two end effectors have been solved.

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Dell’Accio, Francesco, Filomena Di Tommaso, and Federico Nudo. "Constrained mock-Chebyshev least squares quadrature." Applied Mathematics Letters, July 2022, 108328. http://dx.doi.org/10.1016/j.aml.2022.108328.

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Dell’Accio, Francesco, Domenico Mezzanotte, Federico Nudo, and Donatella Occorsio. "Product integration rules by the constrained mock-Chebyshev least squares operator." BIT Numerical Mathematics 63, no. 2 (April 3, 2023). http://dx.doi.org/10.1007/s10543-023-00968-w.

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AbstractIn this paper we consider the problem of the approximation of definite integrals on finite intervals for integrand functions showing some kind of “pathological” behavior, e.g. “nearly” singular functions, highly oscillating functions, weakly singular functions, etc. In particular, we introduce and study a product rule based on equally spaced nodes and on the constrained mock-Chebyshev least squares operator. Like other polynomial or rational approximation methods, this operator was recently introduced in order to defeat the Runge phenomenon that occurs when using polynomial interpolation on large sets of equally spaced points. Unlike methods based on piecewise approximation functions, mainly used in the case of equally spaced nodes, our product rule offers a high efficiency, with performances slightly lower than those of global methods based on orthogonal polynomials in the same spaces of functions. We study the convergence of the product rule and provide error estimates in subspaces of continuous functions. We test the effectiveness of the formula by means of several examples, which confirm the theoretical estimates.

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Qu, Yegao, Yong Chen, Yifan Chen, Xinhua Long, Hongxing Hua, and Guang Meng. "A Domain Decomposition Method for Vibration Analysis of Conical Shells With Uniform and Stepped Thickness." Journal of Vibration and Acoustics 135, no. 1 (February 1, 2013). http://dx.doi.org/10.1115/1.4006753.

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An efficient domain decomposition method is proposed to study the free and forced vibrations of stepped conical shells (SCSs) with arbitrary number of step variations. Conical shells with uniform thickness are treated as special cases of the SCSs. Multilevel partition hierarchy, viz., SCS, shell segment and shell domain, is adopted to accommodate the computing requirement of high-order vibration modes and responses. The interface continuity constraints on common boundaries and geometrical boundaries are incorporated into the system potential functional by means of a modified variational principle and least-squares weighted residual method. Double mixed series, i.e., the Fourier series and Chebyshev orthogonal polynomials, are adopted as admissible displacement functions for each shell domain. To test the convergence, efficiency and accuracy of the present method, free and forced vibrations of uniform thickness conical shells and SCSs are examined under various combinations of classical and nonclassical boundary conditions. The numerical results obtained from the proposed method show good agreement with previously published results and those from the finite element program ANSYS. The computational advantage of the approach can be exploited to gather useful and rapid information about the effects of geometry and boundary conditions on the vibrations of the uniform and stepped conical shells.

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Bailey, A. C., M. Vincenzi, D. Scolnic, J.-C. Cuillandre, J. Rhodes, I. Hook, E. R. Peterson, and B. Popovic. "Type Ia Supernova observations combining data from the Euclid mission and the Vera C. Rubin Observatory." Monthly Notices of the Royal Astronomical Society, July 26, 2023. http://dx.doi.org/10.1093/mnras/stad2179.

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Abstract The Euclid mission will provide first-of-its-kind coverage in the near-infrared over deep (three fields, ∼10–20 square degrees each) and wide (∼10000 square degrees) fields. While the survey is not designed to discover transients, the deep fields will have repeated observations over a two-week span, followed by a gap of roughly six months. In this analysis, we explore how useful the deep field observations will be for measuring properties of Type Ia supernovae (SNe Ia). Using simulations that include Euclid’s planned depth, area and cadence in the deep fields, we calculate that more than 3700 SNe between 0.0 < z < 1.5 will have at least five Euclid detections around peak with signal-to-noise ratio larger than 3. While on their own, Euclid light curves are not good enough to directly constrain distances, when combined with LSST deep field observations, we find that uncertainties on SN distances are reduced by 20–30 % for z < 0.8 and by 40–50% for z > 0.8. Furthermore, we predict how well additional Euclid mock data can be used to constrain a key systematic in SN Ia studies — the size of the luminosity ‘step’ found between SNe hosted in high mass (>1010M⊙) and low mass (<1010M⊙) galaxies. This measurement has unique information in the rest-frame NIR. We predict that if the step is caused by dust, we will be able to measure its reduction in the NIR compared to optical at the 4σ level. We highlight that the LSST and Euclid observing strategies used in this work are still provisional and some level of joint processing is required. Still, these first results are promising, and assuming Euclid begins observations well before the Nancy Roman Space Telescope (Roman), we expect this dataset to be extremely helpful for preparation for Roman itself.

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Snipen, Lars, Inga-Leena Angell, Torbjørn Rognes, and Knut Rudi. "Reduced metagenome sequencing for strain-resolution taxonomic profiles." Microbiome 9, no. 1 (March 29, 2021). http://dx.doi.org/10.1186/s40168-021-01019-8.

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Abstract Background Studies of shifts in microbial community composition has many applications. For studies at species or subspecies levels, the 16S amplicon sequencing lacks resolution and is often replaced by full shotgun sequencing. Due to higher costs, this restricts the number of samples sequenced. As an alternative to a full shotgun sequencing we have investigated the use of Reduced Metagenome Sequencing (RMS) to estimate the composition of a microbial community. This involves the use of double-digested restriction-associated DNA sequencing, which means only a smaller fraction of the genomes are sequenced. The read sets obtained by this approach have properties different from both amplicon and shotgun data, and analysis pipelines for both can either not be used at all or not explore the full potential of RMS data. Results We suggest a procedure for analyzing such data, based on fragment clustering and the use of a constrained ordinary least square de-convolution for estimating the relative abundance of all community members. Mock community datasets show the potential to clearly separate strains even when the 16S is 100% identical, and genome-wide differences is < 0.02, indicating RMS has a very high resolution. From a simulation study, we compare RMS to shotgun sequencing and show that we get improved abundance estimates when the community has many very closely related genomes. From a real dataset of infant guts, we show that RMS is capable of detecting a strain diversity gradient for Escherichia coli across time. Conclusion We find that RMS is a good alternative to either metabarcoding or shotgun sequencing when it comes to resolving microbial communities at the strain level. Like shotgun metagenomics, it requires a good database of reference genomes and is well suited for studies of the human gut or other communities where many reference genomes exist. A data analysis pipeline is offered, as an R package at https://github.com/larssnip/microRMS.

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Journal articles on the topic 'Constrained mock-Chebyshev least squares'

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