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Generalized matrix inversion is not harder than matrix multiplication

✍ Scribed by Marko D. Petković; Predrag S. Stanimirović

Book ID
104006581
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
668 KB
Volume
230
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

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Reverse order laws for generalized inverses of multiple matrix products
✍ Musheng Wei 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 142 KB

In this article we study reverse order laws for generalized inverses and re¯exive generalized inverses of the products of multiple matrices e 1 Y F F F Y e n and the products of generalized inverses and re¯exive generalized inverses of e n Y F F F Y e 1 . By applying the multiple product singular va