Inversion and pseudoinversion of block arrowhead matrices

DOI10.1016/j.amc.2018.09.006zbMath1429.65054OpenAlexW2894500951MaRDI QIDQ2007810

Dejan Kolundžija, Predrag S. Stanimirović, Vasilios N. Katsikis

Publication date: 22 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2018.09.006

zbMATH Keywords

Schur complementsymbolic computationMoore-Penrose inversematrix inverseblock arrowhead matrix

Mathematics Subject Classification ID

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

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Uses Software

• Mathematica

Cites Work

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• Least squares solutions of the matrix equation \(AXB+CYD=E\) with the least norm for symmetric arrowhead matrices
• Computation of the generalized inverse of a polynomial matrix and applications
• A hub matrix theory and applications to wireless communications
• High performance inverse preconditioning
• A practical factorization of a Schur complement for PDE-constrained distributed optimal control
• High performance finite element approximate inverse preconditioning
• Bounds for eigenvalues of arrowhead matrices and their applications to hub matrices and wireless communications
• Report on test matrices for generalized inverses
• The use of a refined error bound when updating eigenvalues of tridiagonals
• Sherman-Morrison-Woodbury-formula-based algorithms for the surface smoothing problem
• A Schur complement approach to a general extrapolation algorithm
• On the solution of boundary value problems by using fast generalized approximate inverse banded matrix techniques
• The Schur complement and its applications
• An explicit formula for the inverse of arrowhead and doubly arrow matrices
• Solving symmetric arrowhead and special tridiagonal linear systems by fast approximate inverse preconditioning
• Pseudo-Schur complements and their properties
• Some Schur complement identities and applications to matrix extrapolation methods
• Expressions for the Moore-Penrose inverse of block matrices involving the Schur complement
• Least-squares solutions of the matrix equations \(A X B + C Y D = H\) and \(A X B + C X D = H\) for symmetric arrowhead matrices and associated approximation problems
• An efficient method for computing the inverse of arrowhead matrices
• Updating the Inverse of a Matrix
• An approximate inverse matrix technique for arrowhead matrices
• Associating hub‐directed multigraphs to arrowhead matrices
• Computational Science and Its Applications – ICCSA 2004
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• A Generalization of the Schur Complement by Means of the Moore–Penrose Inverse
• Generalized Inversion of Modified Matrices
• An Inverse Matrix Adjustment Arising in Discriminant Analysis

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