DELFT UNIVERSITY OF TECHNOLOGY REPORT 07-07 IDR(s): a family of simple and fast algorithms for solving large nonsymmetric linear systems
نویسندگان
چکیده
We present IDR(s), a new family of efficient, short-recurrence methods for large nonsymmetric systems of linear equations. The new methods are based on the Induced Dimension Reduction (IDR) method proposed by Sonneveld in 1980. While state-ofthe-art methods such as Bi-CGSTAB require at most 2N matrix-vector products to compute an exact solution in exact arithmetic, IDR(s) requires at most N + N/s matrix-vector products, with N the problem size and s the dimension of a pre-chosen subspace. We describe the algorithm and the underlying theory and present numerical experiments to illustrate the theoretical properties of the method and its performance for systems arising from different applications. Our experiments show that IDR(s) is competitive with or superior to most Bi-CG-based methods, and outperforms BiCGSTAB when s > 1.
منابع مشابه
IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations
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Delft University of Technology
The Induced Dimension Reduction method [12] was proposed in 1980 as an iterative method for solving large nonsymmetric linear systems of equations. IDR can be considered as the predecessor of methods like CGS (Conjugate Gradient Squared) [9]) and Bi-CGSTAB (Bi-Conjugate Gradients STABilized, [11]). All three methods are based on efficient short recurrences. An important similarity between the m...
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The Induced Dimension Reduction method [12] was proposed in 1980 as an iterative method for solving large nonsymmetric linear systems of equations. IDR can be considered as the predecessor of methods like CGS (Conjugate Gradient Squared) [9]) and Bi-CGSTAB (Bi-Conjugate Gradients STABilized, [11]). All three methods are based on efficient short recurrences. An important similarity between the m...
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IDR(s) [9] and BiCGstab(l) [5] are two of the most efficient short recurrence iterative methods for solving large nonsymmetric linear systems of equations. Which of the two is best depends on the specific problem class. In this paper we derive a new method, that we call IDRstab, that that combines the strengths of IDR(s) and BiCGstab(l). To derive IDRstab we extend the results that we reported ...
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IDR(s) is a family of fast algorithms for iteratively solving large nonsymmetric linear systems [14]. With cluster computing and in particular with Grid computing, the inner product is a bottleneck operation. In this paper, three techniques are combined in order to alleviate this bottleneck. Firstly, the efficient and stable IDR(s) algorithm from [16] is reformulated in such a way that it has a...
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