A class of direct methods for linear systems
type: Item
instance of: scholarly article
title: A class of direct methods for linear systems
zbMATH Open document ID: 0535.65009
DOI: 10.1007/BF01391414
author: József Abaffy
author: C. G. Broyden
author: E. Spedicato
published in: Numerische Mathematik
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/132973
review text: A new class of methods is proposed for solving general (determined or underdetermined, full rank or rank deficient) linear algebraic systems. The class is of direct type methods, the solution being found in a number of steps no larger than the number of equations. The class contains free parameters, say an initial matrix and two vectors to be chosen at each step. A general factorization of the coefficient matrix is implicitly performed by the algorithm and there exist parameter choices implicitly generating orthogonal, LU and Cholesky type factorizations. Computational experiments indicate that some algorithms in this class outperform in accuracy well-known classical methods on some very ill-conditioned problems.
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 3850361
zbMATH Keywords: factorization methods
zbMATH Keywords: computational complexity
zbMATH Keywords: Cholesky factorizations
zbMATH Keywords: Computational experiments
zbMATH Keywords: ill-conditioned problems
MaRDI profile type: Publication
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OpenAlex ID: W1977211467
description: scientific article; zbMATH DE number 3850361