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Numerical Linear Algebra [PDF]
, 2011 Many methods of computational statistics lead to matrix-algebra or numerical-mathematics problems. For example, the least squares method in linear regression reduces to solving a system of linear equations, see Chap. III.8. The principal components method is based on finding eigenvalues and eigenvectors of a matrix, see Chap. III.6.
Čížek, Pavel, Čížková, Lenka
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A Simple and Practical Linear Algebra Library Interface with Static Size Checking [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime errors. While
Akinori Abe, Eijiro Sumii
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Mathematics, 2023 In this paper, we present a numerical linear algebra analytical study of some schemes for the Bertozzi–Esedoglu–Gillette–Cahn–Hilliard equation. Both 1D and 2D finite difference discretizations in space are proposed with semi-implicit and implicit ...
Yahia Awad +2 more
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Usage of computer algebra in teaching process
Lietuvos Matematikos Rinkinys, 1998 This work was intended to motivate the necessity of intensive training of mathematics utilising the computer algebra MAPLE in Lithuanian Military Academy.
Aleksas Domarkas +4 more
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Block-encoding dense and full-rank kernels using hierarchical matrices: applications in quantum numerical linear algebra [PDF]
Quantum, 2022 Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of the matrix of interest, which is a strong assumption when the matrix is not sparse.
Quynh T. Nguyen +2 more
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Recursive Matrix Calculation Paradigm by the Example of Structured Matrix
Information, 2020 In this paper, we derive recursive algorithms for calculating the determinant and inverse of the generalized Vandermonde matrix. The main advantage of the recursive algorithms is the fact that the computational complexity of the presented algorithm is ...
Jerzy S. Respondek
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Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs
EURASIP Journal on Advances in Signal Processing, 2007 Numerical linear algebra algorithms use the inherent elegance of matrix formulations and are usually implemented using C/C++ floating point representation.
Gene Frantz +2 more
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Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra [PDF]
, 2017 We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of randomized iterative ...
Lim, Lek-Heng, Weare, Jonathan
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ABOUT THE VALUES OF THE PARAMETERS THAT DESCRIBE THE NEWTONIAN PROBLEM OF THE EIGHT BODIES
Acta et Commentationes: Ştiinţe Exacte şi ale Naturii, 2020 We consider the Newtonian restricted eight bodies problem with incomplete symmetry. We investigate the stability of some con gurations of this problem. The values of the parameters that describe the Newtonian problem of the eight bodies are investigate ...
Elena CEBOTARU
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Preconditioning and convergence in the right norm [PDF]
, 2007 The convergence of numerical approximations to the solutions of differential equations is a key aspect of Numerical Analysis and Scientific Computing.
Wathen, A. J.
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