Acceleration of a preconditioning method for ill-conditioned dense linear systems by use of a BLAS-based method

Yuka Kobayashi, Takeshi Ogita, Katsuhisa Ozaki

研究成果: Article

抄録

We are interested in accurate numerical solutions of ill-conditioned linear systems using floating-point arithmetic. Recently, we proposed a preconditioning method to reduce the condition numbers of coefficient matrices. The method utilizes an LU factorization obtained in working precision arithmetic and requires matrix multiplication in quadruple precision arithmetic. In this note, we aim to accelerate the preconditioning method from a practical point of view. For this purpose, we apply a more efficient method of accurate matrix multiplication based on BLAS in the preconditioning method. We demonstrate excellent performance of the BLAS-based preconditioning method by numerical experiments.

元の言語English
ページ(範囲)15-23
ページ数9
ジャーナルReliable Computing
25
出版物ステータスPublished - 2017

Fingerprint

Linear systems
Digital arithmetic
Factorization
Experiments

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics

これを引用

@article{58974679d88f4a01977644b5d7a0b368,
title = "Acceleration of a preconditioning method for ill-conditioned dense linear systems by use of a BLAS-based method",
abstract = "We are interested in accurate numerical solutions of ill-conditioned linear systems using floating-point arithmetic. Recently, we proposed a preconditioning method to reduce the condition numbers of coefficient matrices. The method utilizes an LU factorization obtained in working precision arithmetic and requires matrix multiplication in quadruple precision arithmetic. In this note, we aim to accelerate the preconditioning method from a practical point of view. For this purpose, we apply a more efficient method of accurate matrix multiplication based on BLAS in the preconditioning method. We demonstrate excellent performance of the BLAS-based preconditioning method by numerical experiments.",
keywords = "Floating-point arithmetic, Ill-conditioned linear systems, Preconditioning method",
author = "Yuka Kobayashi and Takeshi Ogita and Katsuhisa Ozaki",
year = "2017",
language = "English",
volume = "25",
pages = "15--23",
journal = "Reliable Computing",
issn = "1385-3139",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Acceleration of a preconditioning method for ill-conditioned dense linear systems by use of a BLAS-based method

AU - Kobayashi, Yuka

AU - Ogita, Takeshi

AU - Ozaki, Katsuhisa

PY - 2017

Y1 - 2017

N2 - We are interested in accurate numerical solutions of ill-conditioned linear systems using floating-point arithmetic. Recently, we proposed a preconditioning method to reduce the condition numbers of coefficient matrices. The method utilizes an LU factorization obtained in working precision arithmetic and requires matrix multiplication in quadruple precision arithmetic. In this note, we aim to accelerate the preconditioning method from a practical point of view. For this purpose, we apply a more efficient method of accurate matrix multiplication based on BLAS in the preconditioning method. We demonstrate excellent performance of the BLAS-based preconditioning method by numerical experiments.

AB - We are interested in accurate numerical solutions of ill-conditioned linear systems using floating-point arithmetic. Recently, we proposed a preconditioning method to reduce the condition numbers of coefficient matrices. The method utilizes an LU factorization obtained in working precision arithmetic and requires matrix multiplication in quadruple precision arithmetic. In this note, we aim to accelerate the preconditioning method from a practical point of view. For this purpose, we apply a more efficient method of accurate matrix multiplication based on BLAS in the preconditioning method. We demonstrate excellent performance of the BLAS-based preconditioning method by numerical experiments.

KW - Floating-point arithmetic

KW - Ill-conditioned linear systems

KW - Preconditioning method

UR - http://www.scopus.com/inward/record.url?scp=85021959155&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021959155&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85021959155

VL - 25

SP - 15

EP - 23

JO - Reliable Computing

JF - Reliable Computing

SN - 1385-3139

ER -