### Abstract

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.

Language | English |
---|---|

Pages | 148-167 |

Number of pages | 20 |

Journal | Reliable Computing |

Volume | 25 |

State | Published - 2017 |

### Fingerprint

### Keywords

- Linear systems
- Test problems
- Verified numerical computations

### ASJC Scopus subject areas

- Software
- Computational Mathematics
- Applied Mathematics

### Cite this

*Reliable Computing*,

*25*, 148-167.

**Generation of linear systems with specified solutions for numerical experiments.** / Ozaki, Katsuhisa; Ogita, Takeshi.

Research output: Research - peer-review › Article

*Reliable Computing*, vol 25, pp. 148-167.

}

TY - JOUR

T1 - Generation of linear systems with specified solutions for numerical experiments

AU - Ozaki,Katsuhisa

AU - Ogita,Takeshi

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Linear systems

KW - Test problems

KW - Verified numerical computations

UR - http://www.scopus.com/inward/record.url?scp=85031094832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031094832&partnerID=8YFLogxK

M3 - Article

VL - 25

SP - 148

EP - 167

JO - Reliable Computing

T2 - Reliable Computing

JF - Reliable Computing

SN - 1385-3139

ER -