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- W2049205812 abstract "Y12M is package for the solution of large and sparse systems of linear algebraic equations developed at RECKU.‡ Gaussian elimination and pivotal interchanges are used to factorize the matrix of the system into two triangular matrices. The pivotal strategy used depends on two parameters: u—the stability factor and T—the drop-tolerance. An attempt to control the magnitude of the non-zero elements in order to avoid overflows or underflows and to detect singularities is carried out during the process of the factorization. Iterative refinement of the first solution may be performed. It is verified (by a large set of numerical examples) that the use of iterative refinement combined with a large drop-tolerance and/or with a large stability factor is often very successful in the case where the matrix of the system is sparse. Not only is the accuracy normally greater and the storage required often reduced, but also the factorization time is considerably decreased so that the total computing time for the solution of the system with iterative refinement is smaller than the total computing time for the solution of the system without iterative refinement. Frequently the mathematical models of chemical problems lead (after the time discretization) to very long sequences of large and sparse algebraic systems. The package has successfully been used in the solution of such sequences arising in the theory of nuclear magnetic resonance spectroscopy." @default.
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- W2049205812 date "1980-01-01" @default.
- W2049205812 modified "2023-09-23" @default.
- W2049205812 title "Implementation of an iterative refinement option in a code for large and sparse systems" @default.
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