Iterative methods for Robbins problems

Andy C. Ho; Michael K. Ng

doi:10.1016/j.amc.2004.04.025

Iterative methods for Robbins problems

Andy C. Ho, Michael K. Ng^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

4 Citations (Scopus)

Abstract

Preconditioned iterative methods are described for the solution of an elliptic partial differential equation over an unit square region with Robbins boundary conditions. Transform based preconditioners are constructed and analyzed. The motivation is to exploit the fast inversion of transform based systems via the fast transform. We prove that transform based preconditioners can be chosen so that the condition number of the preconditioned system can be reduced from O(n²) to O(1). Numerical results are reported to illustrate the effectiveness of the preconditioners.

Original language	English
Pages (from-to)	103-125
Number of pages	23
Journal	Applied Mathematics and Computation
Volume	165
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2004.04.025
Publication status	Published - 6 Jun 2005

Scopus Subject Areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2004.04.025

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title = "Iterative methods for Robbins problems",

abstract = "Preconditioned iterative methods are described for the solution of an elliptic partial differential equation over an unit square region with Robbins boundary conditions. Transform based preconditioners are constructed and analyzed. The motivation is to exploit the fast inversion of transform based systems via the fast transform. We prove that transform based preconditioners can be chosen so that the condition number of the preconditioned system can be reduced from O(n2) to O(1). Numerical results are reported to illustrate the effectiveness of the preconditioners.",

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AU - Ho, Andy C.

AU - Ng, Michael K.

PY - 2005/6/6

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N2 - Preconditioned iterative methods are described for the solution of an elliptic partial differential equation over an unit square region with Robbins boundary conditions. Transform based preconditioners are constructed and analyzed. The motivation is to exploit the fast inversion of transform based systems via the fast transform. We prove that transform based preconditioners can be chosen so that the condition number of the preconditioned system can be reduced from O(n2) to O(1). Numerical results are reported to illustrate the effectiveness of the preconditioners.

AB - Preconditioned iterative methods are described for the solution of an elliptic partial differential equation over an unit square region with Robbins boundary conditions. Transform based preconditioners are constructed and analyzed. The motivation is to exploit the fast inversion of transform based systems via the fast transform. We prove that transform based preconditioners can be chosen so that the condition number of the preconditioned system can be reduced from O(n2) to O(1). Numerical results are reported to illustrate the effectiveness of the preconditioners.

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UR - https://www.sciencedirect.com/science/article/pii/S0096300304003650?via%3Dihub

U2 - 10.1016/j.amc.2004.04.025

DO - 10.1016/j.amc.2004.04.025

M3 - Journal article

AN - SCOPUS:17444417455

SN - 0096-3003

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SP - 103

EP - 125

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

Iterative methods for Robbins problems

Abstract

Scopus Subject Areas

UN SDGs

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