Generation of linear systems with specified solutions for numerical experiments

Katsuhisa Ozaki, Takeshi Ogita

Research output: Contribution to journalArticle


The goal of this paper is to generate problems to test solvers for linear systems. Assume that a coefficient matrix A and a right-hand side vector b are given. If numerical computations are used to solve a linear system Ax = b, computed results are usually different from the exact solution due to accumulation of rounding errors. We propose a method to produce a coefficient matrix A and a right-hand side vector b such that the exact solution x is known. The method is useful for examining the accuracy of computed results obtained by some numerical algorithms, and it is useful for checking overestimation of the error bounds obtained by verified numerical computations.

Original languageEnglish
Pages (from-to)148-167
Number of pages20
JournalReliable Computing
Publication statusPublished - 2017



  • Linear systems
  • Test problems
  • Verified numerical computations

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics

Cite this