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1978•International Journal of Computer MathematicsRequires access

A self correcting conjugate gradient algorithm

Avinoam Perry

Open publisher page 12 citations

Abstract

In this paper we develop a new procedure for constructing a conjugate gradient direction equation. The new equation is a linear combination of two orthogonal vectors one of which is the negative gradient. This procedure is reduced to the method of Polak-Ribiere whenever line search is perfectly accurate. Otherwise, as reflected by our computational results, the method is more effective than any other conjugate gradient algorithm we have tested.

About this research paper

What this paper is about

In this paper we develop a new procedure for constructing a conjugate gradient direction equation. The new equation is a linear combination of two orthogonal vectors one of which is the negative gradient. This procedure is reduced to the method of Polak-Ribiere whenever line search is perfectly accurate. Otherwise, as reflected by our computational results, the method is more effective than any other conjugate gradient algorithm we have tested.

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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper we develop a new procedure for constructing a conjugate gradient direction equation. The new equation is a linear combination of two orthogonal vectors one of which is the negative gradient. This procedure is reduced to the method of Polak-Ribiere whenever line search is perfectly accurate. Otherwise, as reflected by our computational results, the method is more effective than any other conjugate gradient algorithm we have tested.

Key concepts: Conjugate gradient method, Derivation of the conjugate gradient method, Conjugate residual method, Nonlinear conjugate gradient method, Biconjugate gradient method, Mathematics, Gradient method, Algorithm

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