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• W2006452217 abstract "We consider the iterative solution of large sparse linear systems of equations arising from elliptic and parabolic partial differential equations in two or three space dimensions. Specifically, we focus our attention on nonsymmetric systems of equations whose eigenvalues lie on both sides of the imaginary axis, or whose symmetric part is not positive definite. This system of equation is solved using a block Kaczmarz projection method with conjugate gradient acceleration. The algorithm has been designed with special emphasis on its suitability for multiprocessors. In the first part of the paper, we study the numerical properties of the algorithm and compare its performance with other algorithms such as the conjugate gradient method on the normal equations, and conjugate gradient-like schemes such as ORTHOMIN(k), GCR(k) and GMRES(k). We also study the effect of using various preconditioners with these methods. In the second part of the paper, we describe the implementation of our algorithm on the CRAY X-MP/48 multiprocessor, and study its behavior as the number of processors is increased." @default.
• W2006452217 created "2016-06-24" @default.
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• W2006452217 date "1989-02-01" @default.
• W2006452217 modified "2023-09-27" @default.
• W2006452217 title "A projection method for solving nonsymmetric linear systems on multiprocessors" @default.
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• W2006452217 doi "https://doi.org/10.1016/0167-8191(89)90114-2" @default.
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