Tight Enclosures of Solutions of Linear Systems
Takeshi Ogita, Shin’ichi Oishi · International series of numerical mathematics · 2008
This paper is concerned with the problem of verifying the accuracy of an approximate solution of a linear system. A fast method of calculating both lower and upper error bounds of the approximate solution is proposed. By the proposed method, it is possible to obtain the error bounds which are as tight as needed. As a result, it can be verified that the obtained error bounds are of high quality. Numerical results are presented elucidating properties and efficiencies of the proposed verification method.