Name
Abstract | ||
|---|---|---|
Summary. In this paper, we are concerned with a matrix equation
where A is an real matrix and x and b are n-vectors. Assume that an approximate solution is given together with an approximate LU decomposition. We will present fast algorithms for proving nonsingularity of A and for calculating rigorous error bounds for . The emphasis is on rigour of the bounds. The purpose of this paper is to propose different algorithms, the fastest with
flops computational cost for the verification step, the same as for the LU decomposition. The presented algorithms exclusively use library routines for LU decomposition and for all other matrix and vector operations.
|
Year | DOI | Venue |
|---|---|---|
2002 | 10.1007/s002110100310 | Numerische Mathematik |
Keywords | Field | DocType |
matrix equation | Linear algebra,Mathematical optimization,Algebra,Mathematical analysis,Matrix (mathematics),Matrix decomposition,Decomposition method (constraint satisfaction),Stone method,Gauss–Seidel method,Mathematics,LU decomposition,Cholesky decomposition | Journal |
Volume | Issue | ISSN |
90 | 4 | 0029-599X |
Citations | PageRank | References |
19 | 2.38 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shin'ichi Oishi | 1 | 280 | 37.14 |
| Siegfried M. Rump | 2 | 774 | 102.83 |