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Persistent URL http://purl.org/net/epubs/work/10940221
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Record Id 10940221
Title New robust limited-memory incomplete Cholesky preconditioners
Abstract The solution of large sparse linear systems of equations Ax=b is one of the cornerstones of computational science and engineering. In many practical applications the solution of such systems is the single most computationally expensive step. Consequently, reducing the solve time can result in significant savings in the total simulation time. As problem sizes grow ever larger, it is necessary to use iterative methods but such methods depend heavily of the availability of suitable preconditioners. An important class of preconditioners for symmetric systems is represented by incomplete Cholesky (IC) factorizations, that is, factorizations of the form LL^T in which some of the fill entries (entries that were zero in A) that would occur in a complete factorization are ignored. Over the last fifty years, many different algorithms for computing incomplete factorizations have been proposed and used to solve problems from a wide range of application areas. This talk focuses on the design and development of a new robust and efficient general-purpose incomplete Cholesky factorization package HSL_MI28, which is available within the HSL mathematical software library. It implements a limited memory approach that exploits ideas from the positive semidefinite Tismenetsky-Kaporin modification scheme and, through the incorporation of intermediate memory, is a generalisation of the widely-used ICFS algorithm of Lin and Mor'e. Both the sparsity density of the incomplete factor and the amount of memory used in its computation are under the user's control. The performance of HSL_MI28 is demonstrated using extensive numerical experiments involving a large set of test problems arising from a wide range of real-world applications. They illustrate the significant advantage of employing a modest amount of intermediate memory and that, with limited memory, high quality yet sparse general-purpose preconditioners are obtained.
Organisation STFC , SCI-COMP , SCI-COMP-CM
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Language English (EN)
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Presentation Presented at Computational linear algebra and optimization for the Digital Economy, ICMS, Edinburgh, UK, 31 Oct 2013 - 1 Nov 2013. Edinburgh13.pdf 2013