Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations
From MaRDI portal
Publication:4210271
DOI10.1137/S089547989629849XzbMath0917.15009MaRDI QIDQ4210271
Publication date: 21 September 1998
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
eigenvaluemultiplicative perturbationsingular valuegraded matrixrelative distancerelative perturbation theory
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Numerical computation of matrix norms, conditioning, scaling (65F35)
Related Items (39)
A Schatten-\(q\) low-rank matrix perturbation analysis via perturbation projection error bound ⋮ Multiplicative relative perturbation bounds of eigenvalues for diagonalizable matrices ⋮ Multiplicative perturbation theory of the Moore-Penrose inverse and the least squares problem ⋮ Optimal sparse eigenspace and low-rank density matrix estimation for quantum systems ⋮ New upper bounds for the spectral variation of a general matrix ⋮ Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework ⋮ On the variation of the spectrum of a Hermitian matrix ⋮ Accurate inverses for computing eigenvalues of extremely ill-conditioned matrices and differential operators ⋮ A fast randomized algorithm for computing an approximate null space ⋮ Euclidean Representation of Low-Rank Matrices and Its Geometric Properties ⋮ The \(\operatorname{Tan}2\Theta \) theorem for indefinite quadratic forms ⋮ Residual bounds for some or all singular values ⋮ Multiplicative perturbation bounds for spectral and singular value decompositions ⋮ A further analysis of backward error in polynomial deflation ⋮ Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices ⋮ Optimal perturbation bounds for the Hermitian eigenvalue problem ⋮ Relative perturbation theory for hyperbolic eigenvalue problem ⋮ Relatively robust representations of symmetric tridiagonals ⋮ An implementation of the dqds algorithm (positive case) ⋮ Perturbation analysis for the Takagi vector matrix ⋮ Barrlund's distance function and quasiconformal maps ⋮ Large volatility matrix estimation with factor-based diffusion model for high-frequency financial data ⋮ Two perturbation bounds for singular values and eigenvalues ⋮ Backward Error Analysis for an Eigenproblem Involving Two Classes of Matrices ⋮ A new weighted metric: the relative metric. II ⋮ New perturbation bounds for the spectrum of a normal matrix ⋮ Backward errors for eigenproblem of two kinds of structured matrices ⋮ Relative residual bounds for indefinite Hermitian matrices ⋮ Relative perturbation bounds for eigenpairs of diagonalizable matrices ⋮ On an eigenvector-dependent nonlinear eigenvalue problem from the perspective of relative perturbation theory ⋮ LARGE SAMPLE PROPERTIES OF BAYESIAN ESTIMATION OF SPATIAL ECONOMETRIC MODELS ⋮ Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices ⋮ First Order Asymptotic Expansions for Eigenvalues of Multiplicatively Perturbed Matrices ⋮ Relative perturbation theory. IV: \(\sin 2\theta\) theorems ⋮ Absolute and relative Weyl theorems for generalized eigenvalue problems ⋮ Relative Perturbation Analysis for Eigenvalues and Singular Values of Totally Nonpositive Matrices ⋮ An overview of relative \(\sin\Theta\) theorems for invariant subspaces of complex matrices ⋮ Relative perturbation theory for hyperbolic singular value problem ⋮ A new weighted metric: the relative metric. I
Uses Software
This page was built for publication: Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations
