Name
Abstract | ||
|---|---|---|
The rational Arnoldi process is a popular method for the computation of a few eigenvalues of a large non-Hermitian matrix A is an element of C-nxn and for the approximation of matrix functions. The method is particularly attractive when the rational functions that determine the process have only few distinct poles zj is an element of C, because then few factorizations of matrices of the form A-z(j)I have to be computed. We discuss recursion relations for orthogonal bases of rational Krylov subspaces determined by rational functions with few distinct poles. These recursion formulas yield a new implementation of the rational Arnoldi process. Applications of the rational Arnoldi process to the approximation of matrix functions as well as to the computation of eigenvalues and pseudospectra of A are described. The new implementation is compared to several available implementations. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1002/nla.2065 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS |
Keywords | Field | DocType |
eigenvalue,matrix function,rational Arnoldi,recursion relation,pseudospectrum | Elliptic rational functions,Pseudospectrum,Algebra,Mathematical analysis,Arnoldi iteration,Matrix (mathematics),Matrix function,Rational function,Mathematics,Eigenvalues and eigenvectors,Recursion | Journal |
Volume | Issue | ISSN |
23.0 | 6.0 | 1070-5325 |
Citations | PageRank | References |
1 | 0.37 | 0 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Miroslav S. Pranic | 1 | 20 | 3.64 |
| Lothar Reichel | 2 | 453 | 95.02 |
| Giuseppe Rodriguez | 3 | 197 | 29.43 |
| Zhengsheng Wang | 4 | 1 | 1.04 |
| Xuebo Yu | 5 | 4 | 0.79 |