Preconditioning random Toeplitz systems

Wen Fong Ke; King Fai Lai; Tsung Lin Lee; Ngai Ching Wong

Preconditioning random Toeplitz systems

Wen Fong Ke, King Fai Lai, Tsung Lin Lee, Ngai Ching Wong

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

It can be very slow in solving large Toeplitz system T_nx = b by the conjugate gradient method (CG), when the eigenvalues of T_n split apart. The preconditioning of a Toeplitz operator by the Strang circulants has been shown to be very efficient. In this paper, we study the applicability of the preconditioning method when a random noise exists. Together with rigorous discussions in theory, numerical examples are also given.

Original language	English
Pages (from-to)	757-770
Number of pages	14
Journal	Journal of Nonlinear and Convex Analysis
Volume	17
Issue number	4
Publication status	Published - 2016

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology
Control and Optimization
Applied Mathematics

Cite this

@article{49378227d982476d9e2d863cb41a16a3,

title = "Preconditioning random Toeplitz systems",

abstract = "It can be very slow in solving large Toeplitz system Tnx = b by the conjugate gradient method (CG), when the eigenvalues of Tn split apart. The preconditioning of a Toeplitz operator by the Strang circulants has been shown to be very efficient. In this paper, we study the applicability of the preconditioning method when a random noise exists. Together with rigorous discussions in theory, numerical examples are also given.",

author = "Ke, {Wen Fong} and Lai, {King Fai} and Lee, {Tsung Lin} and Wong, {Ngai Ching}",

note = "Publisher Copyright: {\textcopyright} 2016.",

year = "2016",

language = "English",

volume = "17",

pages = "757--770",

journal = "Journal of Nonlinear and Convex Analysis",

issn = "1345-4773",

publisher = "Yokohama Publishers",

number = "4",

}

TY - JOUR

T1 - Preconditioning random Toeplitz systems

AU - Ke, Wen Fong

AU - Lai, King Fai

AU - Lee, Tsung Lin

AU - Wong, Ngai Ching

PY - 2016

Y1 - 2016

N2 - It can be very slow in solving large Toeplitz system Tnx = b by the conjugate gradient method (CG), when the eigenvalues of Tn split apart. The preconditioning of a Toeplitz operator by the Strang circulants has been shown to be very efficient. In this paper, we study the applicability of the preconditioning method when a random noise exists. Together with rigorous discussions in theory, numerical examples are also given.

AB - It can be very slow in solving large Toeplitz system Tnx = b by the conjugate gradient method (CG), when the eigenvalues of Tn split apart. The preconditioning of a Toeplitz operator by the Strang circulants has been shown to be very efficient. In this paper, we study the applicability of the preconditioning method when a random noise exists. Together with rigorous discussions in theory, numerical examples are also given.

UR - http://www.scopus.com/inward/record.url?scp=85013996434&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013996434&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85013996434

SN - 1345-4773

VL - 17

SP - 757

EP - 770

JO - Journal of Nonlinear and Convex Analysis

JF - Journal of Nonlinear and Convex Analysis

IS - 4

ER -

Preconditioning random Toeplitz systems

Abstract

All Science Journal Classification (ASJC) codes

Other files and links

Fingerprint

Cite this