 Method for verifying solutions of sparse linear systems with general coefficientsTakeshi Terao and Katsuhisa Ozaki Applied Mathematics and Computation, 2025, vol. 490, issue C Abstract: This paper proposes a verification method for sparse linear systems Ax=b with general and nonsingular coefficient matrices. A verification method produces the error bound for a given approximate solution. Practical methods use one of two approaches. One approach is to verify the computed solution of the normal equation ATAx=ATb by exploiting symmetric and positive definiteness; however, the condition number of ATA is the square of that for A. The other approach applies an approximate inverse of A; however, the approximate inverse of A may be dense even if A is sparse. Additionally, several other methods have been proposed; however, they are considered impractical due to various issues. Here, this paper provides a computing method for verified error bounds using the previous verification method and the latest equilibration. The proposed method can reduce the fill-in and is applicable to many problems. Moreover, we will show the efficiency of an iterative refinement method to obtain accurate solutions. Keywords: Verified numerical computation; Sparse linear system; Minimum singular value; Accurate computation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006659 DOI: 10.1016/j.amc.2024.129204 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.