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ChebStaBlkCG: A block variant of ChebFilterCG
Author(s) -
Sadkane Miloud,
Touhami Ahmed
Publication year - 2019
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2227
Subject(s) - mathematics , conjugate gradient method , chebyshev filter , chebyshev polynomials , convergence (economics) , block (permutation group theory) , eigenvalues and eigenvectors , derivation of the conjugate gradient method , chebyshev equation , conjugate residual method , chebyshev iteration , linear system , set (abstract data type) , algorithm , filter (signal processing) , combinatorics , gradient descent , computer science , mathematical analysis , orthogonal polynomials , classical orthogonal polynomials , physics , quantum mechanics , machine learning , artificial neural network , economics , programming language , economic growth , computer vision
Summary The behavior of ChebFilterCG (an algorithm that combines the Chebyshev filter and Conjugate Gradient) applied to systems with unfavorable eigenvalue distribution is examined. To improve the convergence, a hybrid approach combining a stabilized version of the block conjugated gradient with Chebyshev polynomials as preconditioners (ChebStaBlkCG) is proposed. The performance of ChebStaBlkCG is illustrated and validated on a set of linear systems. It is shown how ChebStaBlkCG can be used to accelerate the block Cimmino method and to solve linear systems with multiple right‐hand sides.