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Some large-scale matrix computation problems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bai, Zhaojun Fahey, Mark R. Golub, Gene H. |
| Copyright Year | 1996 |
| Abstract | Abstract There are numerous applications in physics, statistics and electrical circuit simulation where it is required to bound entries and the trace of the inverse and the determinant of a large sparse matrix. All these computational tasks are related to the central mathematical problem studied in this paper, namely, bounding the bilinear form u T f(A) v for a given matrix A and vectors u and v , where f is a given smooth function and is defined on the spectrum of A. We will study a practical numerical algorithm for bounding the bilinear form, where the matrix A is only referenced through matrix-vector multiplications. A Monte Carlo method is also presented to efficiently estimate the trace of the inverse and the determinant of a large sparse matrix. |
| Starting Page | 71 |
| Ending Page | 89 |
| Page Count | 19 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/0377-0427(96)00018-0 |
| Volume Number | 74 |
| Alternate Webpage(s) | http://web.cs.ucdavis.edu/~bai/publications/baifaheygolub96.pdf |
| Alternate Webpage(s) | http://www.cs.ucdavis.edu/~bai/publications/baifaheygolub96.pdf |
| Alternate Webpage(s) | http://www.ms.uky.edu/~mrfahey/paperticam.ps |
| Alternate Webpage(s) | https://doi.org/10.1016/0377-0427%2896%2900018-0 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
