Generalized matrix inversion is not harder than matrix multiplication

Starting from the Strassen method for rapid matrix multiplication and inversion as well as from the recursive Cholesky factorization algorithm, we introduced a completely block recursive algorithm for generalized Cholesky factorization of a given symmetric, positive semi-definite matrix A ∈ R n × n...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 230; no. 1; pp. 270 - 282
Main Authors: PETKOVIC, Marko D, STANIMIROVIC, Predrag S
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 01.08.2009
Elsevier
Subjects:
Cholesky factorization
Complexity analysis
Exact sciences and technology
Generalized inverses
Mathematical analysis
Mathematics
Moore–Penrose inverse
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Sequences, series, summability
Strassen method
Complexity analysis
Generalized inverses
Strassen method
Moore–Penrose inverse
15A09
Cholesky factorization
Multiplication
Moore Penrose inverse
Numerical linear algebra
Recursive algorithm
Moore-Penrose inverse
Direct method
Numerical analysis
Linear system
Matrix inversion
Applied mathematics
Symmetric matrix
Cholesky method
Factorization method
Positive definite matrix
Recursive method
Matrix method
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:Starting from the Strassen method for rapid matrix multiplication and inversion as well as from the recursive Cholesky factorization algorithm, we introduced a completely block recursive algorithm for generalized Cholesky factorization of a given symmetric, positive semi-definite matrix A ∈ R n × n . We used the Strassen method for matrix inversion together with the recursive generalized Cholesky factorization method, and established an algorithm for computing generalized { 2 , 3 } and { 2 , 4 } inverses. Introduced algorithms are not harder than the matrix–matrix multiplication.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2008.11.012