ScholarLens Back to search
1981•SIAM Journal on Scientific and Statistical ComputingRequires access

On Certain Parallel Toeplitz Linear System Solvers

Joseph F. Grcar, Ahmed Sameh

Open publisher page 19 citations

Abstract

In this paper we describe three algorithms for solving positive-definite banded Toeplitz systems of linear equations on parallel computers. Assuming we have $4mn$ processors, where n is the order of the system and m is the number of super- or subdiagonals, each system may be solved in $O(m\log n)$ time steps. Numerical experiments that compare the behavior of these algorithms in solving pentadiagonal Toeplitz systems are presented.

About this research paper

What this paper is about

In this paper we describe three algorithms for solving positive-definite banded Toeplitz systems of linear equations on parallel computers. Assuming we have $4mn$ processors, where n is the order of the system and m is the number of super- or subdiagonals, each system may be solved in $O(m\log n)$ time steps. Numerical experiments that compare the behavior of these algorithms in solving pentadiagonal Toeplitz systems are presented.

Why it matters

OpenAlex reports 19 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper we describe three algorithms for solving positive-definite banded Toeplitz systems of linear equations on parallel computers. Assuming we have $4mn$ processors, where n is the order of the system and m is the number of super- or subdiagonals, each system may be solved in $O(m\log n)$ time steps. Numerical experiments that compare the behavior of these algorithms in solving pentadiagonal Toeplitz systems are presented.

Key concepts: Toeplitz matrix, Levinson recursion, Linear system, Mathematics, Positive-definite matrix, System of linear equations, Applied mathematics, Algorithm

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
On Certain Parallel Toeplitz Linear System Solvers — Research Paper | ScholarLens