Name
Abstract | ||
|---|---|---|
During the last ten years, Dhillon and Parlett devised a new algorithm (multiple relatively robust representations (MRRR)) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrix $T$ with $\mathcal{O}(n^2)$ cost. It has been incorporated into LAPACK version 3.0 as routine {\sc stegr}.We have discovered that the MRRR algorithm can fail in extreme cases. Sometimes eigenvalues agree to working accuracy and MRRR cannot compute orthogonal eigenvectors for them. In this paper, we describe and analyze these failures and various remedies. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1137/040620746 | SIAM J. Scientific Computing |
Keywords | Field | DocType |
mrrr algorithm,numerically orthogonal eigenvectors,multiple relatively robust representations,new algorithm,orthogonal eigenvectors,tight clusters of eigenvalues,lapack version,various remedy,extreme case,glued matrices,robust representation,wilkinson matrices,symmetric tridiagonal matrix,sc stegr,eigenvectors,eigenvalues,tridiagonal matrix | Tridiagonal matrix,Algebra,Matrix (mathematics),Algorithm,Wilkinson matrix,Symmetric matrix,Numerical analysis,Mathematics,Eigenvalues and eigenvectors | Journal |
Volume | Issue | ISSN |
27 | 2 | 1064-8275 |
Citations | PageRank | References |
13 | 1.26 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Inderjit S. Dhillon | 1 | 7601 | 450.15 |
| Beresford N. Parlett | 2 | 450 | 60.59 |
| Christof Vömel | 3 | 168 | 17.80 |