Accurate Eigensystem Computations by Jacobi Methods

DOI10.1137/S089547989324820XzbMath0835.65057MaRDI QIDQ4842576

Roy Mathias

Publication date: 15 April 1996

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

singular value decompositioneigenvalueserror analysiseigenvectorspositive definite matrixHilbert matrixgraded matrixJacobi's method

Mathematics Subject Classification ID

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

Related Items (15)

Relative perturbation bounds for matrix eigenvalues and singular values ⋮ Asymptotic quadratic convergence of the parallel block-Jacobi EVD algorithm with dynamic ordering for Hermitian matrices ⋮ Asymptotic quadratic convergence of the serial block-Jacobi EVD algorithm for Hermitian matrices ⋮ An SVD-like matrix decomposition and its applications ⋮ Residual bounds for some or all singular values ⋮ A structure-preserving Jacobi algorithm for quaternion Hermitian eigenvalue problems ⋮ Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices ⋮ Approximate eigenvectors as preconditioner ⋮ Convergence to diagonal form of block Jacobi-type methods ⋮ Computing singular values of diagonally dominant matrices to high relative accuracy ⋮ Asymptotic Quadratic Convergence of the Two-Sided Serial and Parallel Block-Jacobi SVD Algorithm ⋮ Relative perturbation theory. IV: \(\sin 2\theta\) theorems ⋮ Implicit standard Jacobi gives high relative accuracy ⋮ One-sided reduction to bidiagonal form ⋮ Highly accurate symmetric eigenvalue decomposition and hyperbolic SVD

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