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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Veröffentlicht in:	Journal of computational and applied mathematics Jg. 230; H. 1; S. 270 - 282
Hauptverfasser:	PETKOVIC, Marko D, STANIMIROVIC, Predrag S
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Kidlington Elsevier B.V 01.08.2009 Elsevier
Schlagworte:	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
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Abstract	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.
AbstractList	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@un@ux@un. 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. 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.
Author	Stanimirović, Predrag S. Petković, Marko D.
Author_xml	– sequence: 1 givenname: Marko D surname: PETKOVIC fullname: PETKOVIC, Marko D organization: University of Niš, Department of Mathematics, Faculty of Science, Višegradska 33, 18000 Niš, Serbia – sequence: 2 givenname: Predrag S surname: STANIMIROVIC fullname: STANIMIROVIC, Predrag S organization: University of Niš, Department of Mathematics, Faculty of Science, Višegradska 33, 18000 Niš, Serbia
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Cites_doi	10.1016/S0893-6080(02)00091-6 10.1147/rd.446.0823 10.1147/rd.416.0737 10.1137/0126022 10.1145/98267.98290 10.1137/S0895479896297744 10.1016/S0747-7171(08)80013-2 10.1080/00207160701582077 10.1007/BF02165411
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Keywords	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
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SubjectTerms	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
Title	Generalized matrix inversion is not harder than matrix multiplication
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