Accurate computation of the smallest eigenvalue of a diagonally dominant $M$-matrix

DOI10.1090/S0025-5718-01-01325-4zbMath0984.65033OpenAlexW2020905775MaRDI QIDQ2759093

Qiang Ye, Attahiru Sule Alfa, Jungong Xue

Publication date: 10 December 2001

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-01-01325-4

zbMATH Keywords

algorithmsnumerical examples\(M\)-matrixdiagonal dominant matrixinverse matrixsmallest eigenvalueentrywise perturbation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (32)

Accurate SVDs of weakly diagonally dominant M-matrices ⋮ ON LATOUCHE–RAMASWAMI'S LOGARITHMIC REDUCTION ALGORITHM FOR QUASI-BIRTH-AND-DEATH PROCESSES ⋮ Accurate solutions of product linear systems associated with rank-structured matrices ⋮ A periodic qd-type reduction for computing eigenvalues of structured matrix products to high relative accuracy ⋮ Accurate eigenvalues of some generalized sign regular matrices via relatively robust representations ⋮ Accurate inverses for computing eigenvalues of extremely ill-conditioned matrices and differential operators ⋮ Accurate and efficient \(LDU\) decomposition of almost diagonally dominant \(Z\)-matrices ⋮ The accurate and efficient solutions of linear systems for generalized sign regular matrices with certain signature ⋮ Accurate solutions of \(M\)-matrix Sylvester equations ⋮ Accurate solutions of \(M\)-matrix algebraic Riccati equations ⋮ Computing singular value decompositions of parameterized matrices with total nonpositivity to high relative accuracy ⋮ Perturbation theory for the LDU factorization and accurate computations for diagonally dominant matrices ⋮ Accurate solutions of diagonally dominant tridiagonal linear systems ⋮ Accurate singular values of a class of parameterized negative matrices ⋮ Accurate Computations and Applications of Some Classes of Matrices ⋮ Eigenvalue bounds for some classes of P -matrices ⋮ Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations ⋮ Accurate solutions of weighted least squares problems associated with rank-structured matrices ⋮ A comparison of error bounds for linear complementarity problems of \(H\)-matrices ⋮ Computing singular values of diagonally dominant matrices to high relative accuracy ⋮ On diagonal dominance of FEM stiffness matrix of fractional Laplacian and maximum principle preserving schemes for the fractional Allen-Cahn equation ⋮ Accurate numerical solution for structured \(M\)-matrix algebraic Riccati equations ⋮ Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices ⋮ Computing eigenvalues of quasi-generalized Vandermonde matrices to high relative accuracy ⋮ Computing exponentials of essentially non-negative matrices entrywise to high relative accuracy ⋮ Accurate numerical solution for shifted \(M\)-matrix algebraic Riccati equations ⋮ Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process ⋮ Relative Perturbation Analysis for Eigenvalues and Singular Values of Totally Nonpositive Matrices ⋮ Highly Accurate Latouche-Ramaswami Logarithmic Reduction Algorithm for Quasi-Birth-and-Death Process ⋮ Accurate Computation of Generalized Eigenvalues of Regular SR-BP Pairs ⋮ A positivity preserving inexact Noda iteration for computing the smallest eigenpair of a large irreducible \(M\)-matrix ⋮ Componentwise accurate fluid queue computations using doubling algorithms

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