Name
Abstract | ||
|---|---|---|
For singular linear systems Ax=b, ORTHOMIN(2) is known theoretically to attain the minimum residual min?x?Rn?b-Ax?2 under a certain condition. However, in the actual computation with finite precision arithmetic, the residual is often observed to be reduced further than the theoretically expected level. Therefore, we propose a variant of ORTHOMIN(2), which is mathematically equivalent to the original ORTHOMIN(2) method, but uses recurrence formulas that are different from those of ORTHOMIN(2); they contain alternative expressions for the auxiliary vector and the recurrence coefficients. Although our implementation has the same computational costs as ORTHOMIN(2), numerical experiments on singular systems show that our implementation is more accurate and less affected by rounding errors than ORTHOMIN(2). |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1023/B:NUMA.0000040047.81654.f5 | Numerical Algorithms |
Keywords | Field | DocType |
Krylov subspace method,Orthomin(2) method,singular systems,two-dimensional minimization,minimum residual norm | Residual,Mathematical optimization,Expression (mathematics),Singular linear systems,Mathematical analysis,Singular systems,Rounding,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
36 | 3 | 1572-9265 |
Citations | PageRank | References |
2 | 0.67 | 4 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kuniyoshi Abe | 1 | 17 | 5.45 |
| Shao-Liang Zhang | 2 | 92 | 19.06 |
| Taketomo Mitsui | 3 | 3 | 1.73 |
| Cheng-Hai Jin | 4 | 2 | 0.67 |