Scientific applications of iterative Toeplitz solvers

Michael K. NG; Raymond H. CHAN

doi:10.1007/bf02576004

Scientific applications of iterative Toeplitz solvers

Michael K. NG^*, Raymond H. CHAN

^*Corresponding author for this work

Research output: Journal Publications › Journal Article (refereed) › peer-review

7 Citations (Scopus)

Abstract

Recent research on using the preconditioned conjugate gradient method as an iterative method for solving Toeplitz systems has brought much attention. One of the main important results of this methodology is that the complexity of solving a large class of Toeplitz systems can be reduced to O(nlogn) operations as compared to the O(nlog²n) operations required by fast direct Toeplitz solvers, provided that a suitable preconditioner is chosen under certain conditions on the Toeplitz operator. In this paper, we survey some applications of iterative Toeplitz solvers to Toeplitz-related problems arising from scientific applications. These applications include partial differential equations, queueing networks, signal and image processing, integral equations, and time series analysis.

Original language	English
Pages (from-to)	249-267
Number of pages	19
Journal	Calcolo
Volume	33
Issue number	3
DOIs	https://doi.org/10.1007/bf02576004
Publication status	Published - Sept 1996
Externally published	Yes

Keywords

Differential equations
Integral equations
Preconditioned conjugate gradient methods
Preconditioners
Queueing problems
Signal and image processing
Time series
Toeplitz matrices

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10.1007/bf02576004

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title = "Scientific applications of iterative Toeplitz solvers",

abstract = "Recent research on using the preconditioned conjugate gradient method as an iterative method for solving Toeplitz systems has brought much attention. One of the main important results of this methodology is that the complexity of solving a large class of Toeplitz systems can be reduced to O(nlogn) operations as compared to the O(nlog2n) operations required by fast direct Toeplitz solvers, provided that a suitable preconditioner is chosen under certain conditions on the Toeplitz operator. In this paper, we survey some applications of iterative Toeplitz solvers to Toeplitz-related problems arising from scientific applications. These applications include partial differential equations, queueing networks, signal and image processing, integral equations, and time series analysis.",

keywords = "Differential equations, Integral equations, Preconditioned conjugate gradient methods, Preconditioners, Queueing problems, Signal and image processing, Time series, Toeplitz matrices",

author = "NG, {Michael K.} and CHAN, {Raymond H.}",

year = "1996",

month = sep,

doi = "10.1007/bf02576004",

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volume = "33",

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journal = "Calcolo",

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T1 - Scientific applications of iterative Toeplitz solvers

AU - NG, Michael K.

AU - CHAN, Raymond H.

PY - 1996/9

Y1 - 1996/9

N2 - Recent research on using the preconditioned conjugate gradient method as an iterative method for solving Toeplitz systems has brought much attention. One of the main important results of this methodology is that the complexity of solving a large class of Toeplitz systems can be reduced to O(nlogn) operations as compared to the O(nlog2n) operations required by fast direct Toeplitz solvers, provided that a suitable preconditioner is chosen under certain conditions on the Toeplitz operator. In this paper, we survey some applications of iterative Toeplitz solvers to Toeplitz-related problems arising from scientific applications. These applications include partial differential equations, queueing networks, signal and image processing, integral equations, and time series analysis.

AB - Recent research on using the preconditioned conjugate gradient method as an iterative method for solving Toeplitz systems has brought much attention. One of the main important results of this methodology is that the complexity of solving a large class of Toeplitz systems can be reduced to O(nlogn) operations as compared to the O(nlog2n) operations required by fast direct Toeplitz solvers, provided that a suitable preconditioner is chosen under certain conditions on the Toeplitz operator. In this paper, we survey some applications of iterative Toeplitz solvers to Toeplitz-related problems arising from scientific applications. These applications include partial differential equations, queueing networks, signal and image processing, integral equations, and time series analysis.

KW - Differential equations

KW - Integral equations

KW - Preconditioned conjugate gradient methods

KW - Preconditioners

KW - Queueing problems

KW - Signal and image processing

KW - Time series

KW - Toeplitz matrices

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U2 - 10.1007/bf02576004

DO - 10.1007/bf02576004

M3 - Journal Article (refereed)

AN - SCOPUS:0029693006

SN - 0008-0624

VL - 33

SP - 249

EP - 267

JO - Calcolo

JF - Calcolo

IS - 3

ER -

Scientific applications of iterative Toeplitz solvers

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Keywords

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