Innovation based on Gaussian elimination to compute generalized inverse \(A_{T,S}^{(2)}\)

DOI10.1016/j.camwa.2013.03.011zbMath1391.65051OpenAlexW2060829850MaRDI QIDQ2629423

Xingping Sheng, Guo-Liang Chen

Publication date: 6 July 2016

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2013.03.011

zbMATH Keywords

generalized inverse \(A_{T,S}^{(2)}\)elementary row (column) operationsmultiplications and divisions operations

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

Computing the outer and group inverses through elementary row operations ⋮ Methods of Gauss–Jordan elimination to compute core inverse and dual core inverse ⋮ The Core-EP, Weighted Core-EP Inverse of Matrices and Constrained Systems of Linear Equations ⋮ Computation of weighted Moore-Penrose inverse through Gauss-Jordan elimination on bordered matrices ⋮ An efficient method for computing the outer inverse \(A_{T,S}^{(2)}\) through Gauss-Jordan elimination ⋮ Existence and Representations of Solutions to Some Constrained Systems of Matrix Equations ⋮ The representations and computations of generalized inverses \(A^{(1)}_{T,S}\), \(A^{(1,2)}_{T,S}\) and the group inverse ⋮ An efficient method to compute different types of generalized inverses based on linear transformation ⋮ Two closed novel formulas for the generalized inverse \(A_{T,S}^{(2)}\) of a complex matrix with given rank ⋮ Gauss-Jordan elimination method for computing all types of generalized inverses related to the {1}-inverse

Cites Work

• Unnamed Item
• Gauss-Jordan elimination methods for the Moore-Penrose inverse of a matrix
• The representation and approximations of outer generalized inverses
• New proofs of two representations and minor of generalized inverse \(A_{T,S}^{(2)}\)
• Representation and approximate for generalized inverse \(A_{T,S}^{(2)}\): revisited
• The generalized Bott-Duffin inverse and its applications
• The \(\{\) 2\(\}\)-inverse with applications in statistics
• Partial orders based on outer inverses
• On moment-discretization and least-squares solutions of linear integral equations of the first kind
• Minors of the Moore-Penrose inverse
• Convergence of Newton-like methods for singular operator equations using outer inverses
• A new type of matrix splitting and its applications
• Computing generalized inverses of matrices by iterative methods based on splittings of matrices
• A characterization and representation of the generalized inverse \(A_{T,S}^{(2)}\) and its applications
• Using Gauss-Jordan elimination to compute the index, generalized nullspaces, and Drazin inverse
• The representation and approximation for the generalized inverse \(A^{(2)}_{T,S}\)
• Generalized inverses. Theory and applications.
• Representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\)
• Gauss-Jordan elimination method for computing outer inverses
• The representation and computation of generalized inverse \(A^{(2)}_{T,S}\)
• Full-rank representation of generalized inverse \(A_{T,S}^{(2)}\) and its application
• The representation of generalized inverse \(A_{T,S}^{(2,3)}\) and its applications
• (T,S) splitting methods for computing the generalized inverse and rectangular systems^∗
• A note of computation for M-P inverseA^†
• Determinantal representation of the generalized inverse\bi A_{T,S}^{(2)}over integral domains and its applications
• On determinantal representation for the generalized inverseA(2)T,S and its applications
• Analogs of the adjoint matrix for generalized inverses and corresponding Cramer rules
• Several representations of generalized inverse and their application
• Reflexive generalized inverses and their minors^*
• Iterative methods for computing generalized inverses related with optimization methods
• A geometrical approach on generalized inverses by Neumann-type series