Implicit standard Jacobi gives high relative accuracy
From MaRDI portal
Publication:1034687
DOI10.1007/s00211-009-0240-8zbMath1223.65025OpenAlexW2130485496MaRDI QIDQ1034687
Plamen Koev, Froilán M. Dopico, Juan M. Molera
Publication date: 6 November 2009
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00211-009-0240-8
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Hermitian, skew-Hermitian, and related matrices (15B57) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12)
Related Items (15)
Multiplicative perturbation theory of the Moore-Penrose inverse and the least squares problem ⋮ 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 ⋮ Convergence to Singular Triplets in the Two-Sided Block-Jacobi SVD Algorithm with Dynamic Ordering ⋮ Accurate inverses for computing eigenvalues of extremely ill-conditioned matrices and differential operators ⋮ Three-level parallel J-Jacobi algorithms for Hermitian matrices ⋮ 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 ⋮ Full block \(J\)-Jacobi method for Hermitian matrices ⋮ Novel modifications of parallel Jacobi algorithms ⋮ On the quadratic convergence of the complex HZ method for the positive definite generalized eigenvalue problem ⋮ Convergence to diagonal form of block Jacobi-type methods ⋮ Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices ⋮ Asymptotic Quadratic Convergence of the Two-Sided Serial and Parallel Block-Jacobi SVD Algorithm ⋮ 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
- Unnamed Item
- Unnamed Item
- Accurate eigenvalues of certain sign regular matrices
- Error analysis of QR decompositions by Givens transformations
- Accurate singular values and differential qd algorithms
- A Jacobi eigenreduction algorithm for definite matrix pairs
- Componentwise analysis of direct factorization of real symmetric and Hermitian matrices
- Relative perturbation theory. IV: \(\sin 2\theta\) theorems
- Highly accurate symmetric eigenvalue decomposition and hyperbolic SVD
- Accurate SVDs of weakly diagonally dominant M-matrices
- Computing the singular value decomposition with high relative accuracy
- On computing accurate singular values and eigenvalues of matrices with acyclic graphs
- Accelerating the SVD block-Jacobi method
- Accurate SVDs of polynomial Vandermonde matrices involving orthonormal polynomials
- Handbook series linear algebra. Linear least squares solutions by Householder transformations
- The Jacobi method for real symmetric matrices
- Computing singular values of diagonally dominant matrices to high relative accuracy
- Accurate Singular Values of Bidiagonal Matrices
- New Fast and Accurate Jacobi SVD Algorithm. I
- New Fast and Accurate Jacobi SVD Algorithm. II
- LAPACK Users' Guide
- Jacobi’s Method is More Accurate than QR
- Accurate Computation of the Product-Induced Singular Value Decomposition with Applications
- Relative Perturbation Theory: II. Eigenspace and Singular Subspace Variations
- A posteriori computation of the singular vectors in a preconditioned Jacobi SVD algorithm
- Fast Plane Rotations with Dynamic Scaling
- Implementation of Jacobi Rotations for Accurate Singular Value Computation in Floating Point Arithmetic
- An Orthogonal High Relative Accuracy Algorithm for the Symmetric Eigenproblem
- Accuracy and Stability of Numerical Algorithms
- Accurate Eigensystem Computations by Jacobi Methods
- Relative Perturbation Techniques for Singular Value Problems
- Accurate Singular Value Decompositions of Structured Matrices
- Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices
- Accurate Eigenvalues and SVDs of Totally Nonnegative Matrices
- Accurate Symmetric Rank Revealing and Eigendecompositions of Symmetric Structured Matrices
- Accurate Factorization and Eigenvalue Algorithms for Symmetric DSTU and TSC Matrices
- Convergence of a Block‐Oriented Quasi‐Cyclic Jacobi Method
- Perturbation Theory for Factorizations of LU Type through Series Expansions
This page was built for publication: Implicit standard Jacobi gives high relative accuracy
