Fast Rational Lanczos Method for the Toeplitz Symmetric Positive Semidefinite Matrix Functions

Lei Chen; Lu Zhang; Mengjia Wu; Jianqiang Zhao

Simulation Tools and Techniques. 12th EAI International Conference, SIMUtools 2020, Guiyang, China, August 28-29, 2020, Proceedings, Part I

Research Article

Fast Rational Lanczos Method for the Toeplitz Symmetric Positive Semidefinite Matrix Functions

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@INPROCEEDINGS{10.1007/978-3-030-72792-5_15,
    author={Lei Chen and Lu Zhang and Mengjia Wu and Jianqiang Zhao},
    title={Fast Rational Lanczos Method for the Toeplitz Symmetric Positive Semidefinite Matrix Functions},
    proceedings={Simulation Tools and Techniques. 12th EAI International Conference, SIMUtools 2020, Guiyang, China, August 28-29, 2020, Proceedings, Part I},
    proceedings_a={SIMUTOOLS},
    year={2021},
    month={4},
    keywords={Toeplitz Matrix function Rational lanczos method Gohberg-Semencul formula},
    doi={10.1007/978-3-030-72792-5_15}
}

Lei Chen
Lu Zhang
Mengjia Wu
Jianqiang Zhao
Year: 2021
Fast Rational Lanczos Method for the Toeplitz Symmetric Positive Semidefinite Matrix Functions
SIMUTOOLS
Springer
DOI: 10.1007/978-3-030-72792-5_15

Lei Chen¹, Lu Zhang², Mengjia Wu², Jianqiang Zhao²

1: School of Information Engineering, Xuzhou University of Technology, Xuzhou
2: School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou

Abstract

In this paper, we use the rational Lanczos method to approximate Toeplitz matrix functions, in which the matrices are symmetric positive semidefinite (SPSD). In order to reduce the computational cost, we use the inverse of the Toeplitz matrix and the fast Fourier transform (FFT). Then, we apply this method to solve a heat equation. Numerical examples are given to show the effectiveness of the rational Lanczos method.

Keywords: Toeplitz Matrix function Rational lanczos method Gohberg-Semencul formula

Published: 2021-04-27
Appears in: SpringerLink

: http://dx.doi.org/10.1007/978-3-030-72792-5_15

Fast Rational Lanczos Method for the Toeplitz Symmetric Positive Semidefinite Matrix Functions

Abstract

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