Relative Perturbation Analysis for Eigenvalues and Singular Values of Totally Nonpositive Matrices
From MaRDI portal
Publication:5254388
DOI10.1137/140995702zbMath1328.65089OpenAlexW1987449469MaRDI QIDQ5254388
Publication date: 9 June 2015
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/140995702
Factorization of matrices (15A23) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Special matrices (15B99)
Related Items (15)
On the characterization of totally nonpositive 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 ⋮ On the sensitivity of generators for the QR factorization of quasiseparable matrices with total nonpositivity ⋮ Accurate computation of eigenvalues of generalized sign regular quasi-Said-Ball-Vandermonde matrices ⋮ Total negativity: characterizations and single-vector tests ⋮ Periodic solutions of nonlinear differential systems by the method of averaging. ⋮ Computing singular value decompositions of parameterized matrices with total nonpositivity to high relative accuracy ⋮ Refined upper solution bound of the continuous coupled algebraic Riccati equation ⋮ Extended irreducible Nekrasov matrices as subclasses of irreducible \(H\)-matrices ⋮ Numerical algorithms of the discrete coupled algebraic Riccati equation arising in optimal control systems ⋮ Accurate solutions of weighted least squares problems associated with rank-structured matrices ⋮ Accurate computations of eigenvalues of quasi-Cauchy-Vandermonde matrices ⋮ A qd-type method for computing generalized singular values of BF matrix pairs with sign regularity to high relative accuracy ⋮ Computing eigenvalues of quasi-generalized Vandermonde matrices to high relative accuracy
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Perturbation theory for the LDU factorization and accurate computations for diagonally dominant matrices
- Accurate eigenvalues of certain sign regular matrices
- Total nonpositivity of nonsingular matrices
- Spectral sensitivity of products of bidiagonals
- A matricial description of Neville elimination with applications to total positivity
- Entrywise perturbation theory for diagonally dominant M-matrices with applications
- Perturbation of eigenpairs of factored symmetric tridiagonal matrices
- On nonsingular sign regular matrices
- Accurate SVDs of weakly diagonally dominant M-matrices
- A test and bidiagonal factorization for certain sign regular matrices
- Computing the singular value decomposition with high relative accuracy
- Accurate computation of the smallest eigenvalue of a diagonally dominant $M$-matrix
- A New Perturbation Bound for the LDU Factorization of Diagonally Dominant Matrices
- A stable test for strict sign regularity
- Total Positivity, $QR$ Factorization, and Neville Elimination
- Accurate Computations with Totally Nonnegative Matrices
- $LDU$ Factorization of Nonsingular Totally Nonpositive Matrices
- Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations
- Relative Perturbation Theory: II. Eigenspace and Singular Subspace Variations
- Accuracy and Stability of Numerical Algorithms
- Relative Perturbation Bounds for Eigenvalues of Symmetric Positive Definite Diagonally Dominant Matrices
- Relative Perturbation Theory for Diagonally Dominant Matrices
- On Accurate Computations of the Perron Root
- A Bidiagonal Matrix Determines Its Hyperbolic SVD to Varied Relative Accuracy
- Accurate Eigenvalues and SVDs of Totally Nonnegative Matrices
- Totally positive matrices
This page was built for publication: Relative Perturbation Analysis for Eigenvalues and Singular Values of Totally Nonpositive Matrices
