A fast convergent iterative solver for approximate inverse of matrices

SUMMARY In this paper, a rapid iterative algorithm is proposed to find robust approximations for the inverse of nonsingular matrices. The analysis of convergence reveals that this high‐order method possesses eighth‐order convergence. The interesting point is that, this rate is attained using less nu...

Full description

Saved in:
Bibliographic Details
Published inNumerical linear algebra with applications Vol. 21; no. 3; pp. 439 - 452
Main Author Soleymani, F.
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.05.2014
Wiley Subscription Services, Inc
Subjects
approximate inverse
Approximation
Consistency
Convergence
fast convergent
Inverse
Krylov subspace
Linear algebra
Mathematical models
Moore-Penrose inverse
Multiplication
Solvers
sparse matrices
Stability
Online AccessGet full text

Cover

More Information
Summary:SUMMARY In this paper, a rapid iterative algorithm is proposed to find robust approximations for the inverse of nonsingular matrices. The analysis of convergence reveals that this high‐order method possesses eighth‐order convergence. The interesting point is that, this rate is attained using less number of matrix‐by‐matrix multiplications in contrast to the existing methods of the same type in the literature. The extension of the method for finding Moore–Penrose inverse of singular or rectangular matrices is also presented. Numerical comparisons will be given to show the applicability, stability and consistency of the new scheme by paying special attention on the computational time. Copyright © 2013 John Wiley & Sons, Ltd.
Bibliography:ark:/67375/WNG-9TW2D9DM-S
ArticleID:NLA1890
istex:9B610F9C8AA4B0454B3C94138F9D9979ACAECE5E
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.1890