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2016•Journal of applied mathematics & informaticsOpen access

FAST ONE-PARAMETER RELAXATION METHOD WITH A SCALED PRECONDITIONER FOR SADDLE POINT PROBLEMS

Se‐Young Oh, Jae Heon Yun

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Abstract

In this paper, we first propose a fast one-parameter relaxation (FOPR) method with a scaled preconditioner for solving the saddle point problems, and then we present a formula for finding its optimal parameter. To evaluate the effectiveness of the proposed FOPR method with a scaled preconditioner, numerical experiments are provided by comparing its performance with the existing one or two parameter relaxation methods with optimal parameters such as the SOR-like, the GSOR and the GSSOR methods.

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What this paper is about

In this paper, we first propose a fast one-parameter relaxation (FOPR) method with a scaled preconditioner for solving the saddle point problems, and then we present a formula for finding its optimal parameter. To evaluate the effectiveness of the proposed FOPR method with a scaled preconditioner, numerical experiments are provided by comparing its performance with the existing one or two parameter relaxation methods with optimal parameters such as the SOR-like, the GSOR and the GSSOR methods.

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Available abstract

In this paper, we first propose a fast one-parameter relaxation (FOPR) method with a scaled preconditioner for solving the saddle point problems, and then we present a formula for finding its optimal parameter. To evaluate the effectiveness of the proposed FOPR method with a scaled preconditioner, numerical experiments are provided by comparing its performance with the existing one or two parameter relaxation methods with optimal parameters such as the SOR-like, the GSOR and the GSSOR methods.

Key concepts: Preconditioner, Saddle point, Relaxation (psychology), Mathematics, Saddle, Point (geometry), Applied mathematics, Mathematical optimization

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