On computing accurate singular values and eigenvalues of matrices with acyclic graphs

DOI10.1016/0024-3795(93)90213-8zbMath0770.65021OpenAlexW2065197309MaRDI QIDQ2365723

James W. Demmel, William B. Gragg

Publication date: 29 June 1993

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(93)90213-8

zbMATH Keywords

algorithmbipartite grapheigenvaluesperturbationssingular valuesbidiagonal matrixsymmetric matrices with acyclic graphs

Mathematics Subject Classification ID

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

Related Items (16)

A graph-theoretic model of symmetric Givens operations and its implications ⋮ A periodic qd-type reduction for computing eigenvalues of structured matrix products to high relative accuracy ⋮ Evaluation of small elements of the eigenvectors of certain symmetric tridiagonal matrices with high relative accuracy ⋮ Accurate eigenvalues of some generalized sign regular matrices via relatively robust representations ⋮ A Parallel Algorithm for Computing the Eigenvalues of a Symmetric Tridiagonal Matrix ⋮ 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 ⋮ Relative perturbation bounds for the unitary polar factor ⋮ Factoring matrices with a tree-structured sparsity pattern ⋮ Computing singular values of diagonally dominant matrices to high relative accuracy ⋮ Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices ⋮ Relative perturbation theory. IV: \(\sin 2\theta\) theorems ⋮ A qd-type method for computing generalized singular values of BF matrix pairs with sign regularity to high relative accuracy ⋮ Implicit standard Jacobi gives high relative accuracy ⋮ Computing eigenvalues of quasi-generalized Vandermonde matrices to high relative accuracy ⋮ Highly accurate symmetric eigenvalue decomposition and hyperbolic SVD

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