Roundoff-error analysis of a new class of conjugate-gradient algorithms |
| |
Authors: | H Wo?niakowski |
| |
Institution: | Department of Computer Science Carnegie-Mellon University Pittsburgh, Pennsylvania 15213 USA |
| |
Abstract: | We perform the rounding-error analysis of the conjugate-gradient algorithms for the solution of a large system of linear equations Ax=b where Ais an hermitian and positive definite matrix. We propose a new class of conjugate-gradient algorithms and prove that in the spectral norm the relative error of the computed sequence {xk} (in floating-point arithmetic) depends at worst on ζк, where ζ is the relative computer precision and к is the condition number of A. We show that the residual vectors rk=Axk-b are at worst of order ζк?vA?v ?vxk?v. We p oint out that with iterative refinement these algorithms are numerically stable. If ζк 2 is at most of order unity, then they are also well behaved. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|