Accuracy of two SVD algorithms for \(2\times 2\) triangular matrices

DOI10.1016/j.amc.2008.12.086zbMath1166.65014OpenAlexW2060333799MaRDI QIDQ1015805

Vjeran Hari, Josip Matejaš

Publication date: 30 April 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2008.12.086

zbMATH Keywords

numerical examplessingular value decompositionerror analysispseudoinversestriangular matricesoverdetermined systemsKogbetliantz methodSVD algorithm

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical solutions to overdetermined systems, pseudoinverses (65F20)

Related Items (8)

A Kogbetliantz-type algorithm for the hyperbolic SVD ⋮ The Singular Value Decomposition: Anatomy of Optimizing an Algorithm for Extreme Scale ⋮ The high relative accuracy of the HZ method ⋮ Batched Computation of the Singular Value Decompositions of Order Two by the AVX-512 Vectorization ⋮ Accuracy of the Kogbetliantz method for scaled diagonally dominant triangular matrices ⋮ On high relative accuracy of the Kogbetliantz method ⋮ Convergence to diagonal form of block Jacobi-type methods ⋮ Accuracy of one step of the Falk-Langemeyer method

Uses Software

• LAPACK

Cites Work

• A triangular processor array for computing singular values
• On the quadratic convergence of Kogbetliantz's algorithm for computing the singular value decomposition
• On Kogbetliantz's SVD algorithm in the presence of clusters
• On sharp quadratic convergence bounds for the serial Jacobi methods
• On efficient implementations of Kogbetliantz's algorithm for computing the singular value decomposition
• Linear convergence of the row cyclic Jacobi and Kogbetliantz methods
• Solution of linear equations by diagonalization of coefficients matrix
• The Cyclic Jacobi Method for Computing the Principal Values of a Complex Matrix
• On Jacobi Methods for Singular Value Decompositions
• Jacobi’s Method is More Accurate than QR
• On the Quadratic Convergence of the Serial Singular Value Decomposition Jacobi Methods for Triangular Matrices
• A posteriori computation of the singular vectors in a preconditioned Jacobi SVD algorithm
• Implementation of Jacobi Rotations for Accurate Singular Value Computation in Floating Point Arithmetic
• Numerical Stability of the Parallel Jacobi Method
• On Cyclic Jacobi Methods
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Accuracy of two SVD algorithms for \(2\times 2\) triangular matrices