Computing generalized inverses using LU factorization of matrix product

DOI10.1080/00207160701582077zbMath1158.65029arXiv1104.1697OpenAlexW1766302165MaRDI QIDQ3545676

Predrag S. Stanimirović, Milan B. Tasić

Publication date: 11 December 2008

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.1697

zbMATH Keywords

algorithmcomparison of methodsnumerical examplesMATHEMATICAMAPLEmatrix productsgeneralized inversesMoore-Penrose inverserational matricesCholesky factorizationsDELPHIGrevile's partitioning methodLeVerrier-Faddeev algorithmVISUALBASIC

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09)

Related Items (16)

Computation of generalized inverses by using the \(LDL^{\ast}\) decomposition ⋮ Mixed-type reverse-order laws for \(\{1, 3, 4\}\)-generalized inverses over Hilbert spaces ⋮ Symbolic computation of \(A_{T,S}^{(2)}\)-inverses using QDR factorization ⋮ A Novel Iterative Method for Computing Generalized Inverse ⋮ One-sided weighted outer inverses of tensors ⋮ Representations of generalized inverses via full-rank QDR decomposition ⋮ Computing \(\{2,4\}\) and \(\{2,3\}\)-inverses by using the Sherman-Morrison formula ⋮ Neural network for computing pseudoinverses and outer inverses of complex-valued matrices ⋮ Computation of {2,4} and {2,3}-inverses based on rank-one updates ⋮ Composite outer inverses for rectangular matrices ⋮ Exact solutions and convergence of gradient based dynamical systems for computing outer inverses ⋮ The forward order laws for \(\{1,2,3\}\)- and \(\{1,2,4\}\)-inverses of multiple matrix products ⋮ Generalized matrix inversion is not harder than matrix multiplication ⋮ Computation of generalized inverses using PHP/MySQL environment ⋮ A note on the forward order law for least square \(g\)-inverse of three matrix products ⋮ The forward order laws for {1,2,3}- and {1,2,4}-inverses of a three matrix products

Uses Software

• Maple
• Mathematica

Cites Work

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• Computation of the generalized inverse of a polynomial matrix and applications
• Report on test matrices for generalized inverses
• Generalized inverses of two-variable polynomial matrices and applications
• The computation and application of the generalized inverse via Maple
• A finite algorithm for generalized inverses of polynomial and rational matrices
• The algorithm for computing the Drazin inverses of two-variable polynomial matrices
• Successive matrix squaring algorithm for computing the Drazin inverse
• A finite algorithm for the Drazin inverse of a polynomial matrix
• Generalized inverses. Theory and applications.
• Partitioning method for rational and polynomial matrices
• On the Moore-Penrose generalized inverse matrix
• On the computation of the generalized inverse of a polynomial matrix
• Computation of the inverse of a polynomial matrix and evaluation of its Laurent expansion
• Further results on output control in the servomechanism sense
• Transfer-function matrix synthesis by matrix generalized inverses
• Symbolic computation of the Moore–Penrose inverse using a partitioning method

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