An approximate inverse matrix technique for arrowhead matrices

DOI10.1080/00207169808804734zbMath0933.65031OpenAlexW2134176558MaRDI QIDQ4256047

George A. Gravvanis

Publication date: 20 March 2000

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

Full work available at URL: https://doi.org/10.1080/00207169808804734

zbMATH Keywords

numerical examplespreconditioningparallel computationChebyshev iterationRichardson iteration\(LU\)-factorizationarrowhead matricesapproximate inverse matrix

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (12)

High performance inverse preconditioning ⋮ LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS IN ARROWHEAD FORM ⋮ Explicit approximate inverse preconditioning techniques ⋮ Explicit preconditioned domain decomposition schemes for solving nonlinear boundary value problems. ⋮ Factored approximate inverse preconditioners with dynamic sparsity patterns ⋮ Inversion and pseudoinversion of block arrowhead matrices ⋮ A two-phase preconditioning strategy of sparse approximate inverse for indefinite matrices ⋮ Explicit isomorphic iterative methods for solving arrow-type linear systems ⋮ An explicit formula for the inverse of arrowhead and doubly arrow matrices ⋮ Explicit preconditioned conjugate gradient schemes for solving biharmonic equations ⋮ A sparse approximate inverse preconditioner for parallel preconditioning of general sparse matrices ⋮ An efficient method for computing the inverse of arrowhead matrices

Cites Work

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• Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices
• The numerically stable reconstruction of Jacobi matrices from spectral data
• The use of a refined error bound when updating eigenvalues of tridiagonals
• A Divide and Conquer method for the symmetric tridiagonal eigenproblem
• A three-dimensional explicit preconditioned solver
• The rate of convergence of explicit approximate inverse preconditioning
• QR-Like Algorithms for Symmetric Arrow Matrices
• A class of explicit preconditioned conjugate gradient methods for solving large finite element systems
• Explicit preconditioned methods for solving 3d boundary-value problems by approximate inverse finite element matrix techniques
• Some Modified Matrix Eigenvalue Problems

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