Computing the singular value decompostion of a product of two matrices
SIAM Journal on Scientific and Statistical Computing
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Accurate Computation of the Product-Induced Singular Value Decomposition with Applications
SIAM Journal on Numerical Analysis
Matrix algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
A Jacobi--Davidson Type SVD Method
SIAM Journal on Scientific Computing
Computing the SVD of a General Matrix Product/Quotient
SIAM Journal on Matrix Analysis and Applications
SIAM Review
A periodic Krylov-Schur algorithm for large matrix products
Numerische Mathematik
Hi-index | 7.29 |
We propose a Jacobi-Davidson type method to compute selected eigenpairs of the product eigenvalue problem A"m...A"1x=@lx, where the matrices may be large and sparse. To avoid difficulties caused by a high condition number of the product matrix, we split up the action of the product matrix and work with several search spaces. We generalize the Jacobi-Davidson correction equation and the harmonic and refined extraction for the product eigenvalue problem. Numerical experiments indicate that the method can be used to compute eigenvalues of product matrices with extremely high condition numbers.