Super-fast validated solution of linear systems |
| |
Authors: | Siegfried M Rump Takeshi Ogita |
| |
Institution: | 1. Institute for Realible Computing, Hamburg University of Technology, Schwarzenbergstraße 95, Hamburg 21071, Germany;2. Graduate School of Science and Engineering, Waseda University, 3-4-1 Okubo Shinjuku-ku, Tokyo 169-8555, Japan |
| |
Abstract: | Validated solution of a problem means to compute error bounds for a solution in finite precision. This includes the proof of existence of a solution. The computed error bounds are to be correct including all possible effects of rounding errors. The fastest known validation algorithm for the solution of a system of linear equations requires twice the computing time of a standard (purely) numerical algorithm. In this paper we present a super-fast validation algorithm for linear systems with symmetric positive definite matrix. This means that the entire computing time for the validation algorithm including computation of an approximated solution is the same as for a standard numerical algorithm. Numerical results are presented. |
| |
Keywords: | 65F05 |
本文献已被 ScienceDirect 等数据库收录! |
|