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Simpler Hybrid GMRES

Hualei Liu

Open publisher page 2 citations

Abstract

Abstract. Hybrid GMRES algorithms are effective for solving large nonsymmetric linear systems. GMRES is employed at the first phase to produce iterative polynomials, which will be used at the second phase to implement the Richardson iteration. In the process of GMRES, a least squares problem needs to be solved which involves an upper Hessenberg factorization. Instead of using GMRES, we may use simpler GMRES. Correspondingly, simpler hybrid GMRES algorithms are formulated. It is described how to construct the iterative polynomials from simpler GMRES. The new algorithms avoid the upper Hessenberg factorization so that they are easier to program and require a less amount of work. Numerical examples are conducted to illustrate the good performance of the new algorithms. Key words: linear systems, iterative methods, GMRES, hybrid algorithm. 1.

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What this paper is about

Abstract. Hybrid GMRES algorithms are effective for solving large nonsymmetric linear systems. GMRES is employed at the first phase to produce iterative polynomials, which will be used at the second phase to implement the Richardson iteration. In the process of GMRES, a least squares problem needs to be solved which involves an upper Hessenberg factorization. Instead of using GMRES, we may use simpler GMRES. Correspondingly, simpler hybrid GMRES algorithms are formulated. It is described how to construct the iterative polynomials from simpler GMRES. The new algorithms avoid the upper Hessenberg factorization so that they are easier to program and require a less amount of work. Numerical examples are conducted to illustrate the good performance of the new algorithms. Key words: linear systems, iterative methods, GMRES, hybrid algorithm. 1.

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Available abstract

Abstract. Hybrid GMRES algorithms are effective for solving large nonsymmetric linear systems. GMRES is employed at the first phase to produce iterative polynomials, which will be used at the second phase to implement the Richardson iteration. In the process of GMRES, a least squares problem needs to be solved which involves an upper Hessenberg factorization. Instead of using GMRES, we may use simpler GMRES. Correspondingly, simpler hybrid GMRES algorithms are formulated. It is described how to construct the iterative polynomials from simpler GMRES. The new algorithms avoid the upper Hessenberg factorization so that they are easier to program and require a less amount of work. Numerical examples are conducted to illustrate the good performance of the new algorithms. Key words: linear systems, iterative methods, GMRES, hybrid algorithm. 1.

Key concepts: Generalized minimal residual method, Mathematics, Factorization, Linear system, Iterative method, Algorithm, Computer science, Applied mathematics

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