Symbolic Methods for the Element Preconditioning Technique
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The method of element preconditioning requires the construction of an M-matrix which is as close as possible to a given symmetric positive definite matrix in the spectral sense. In this paper we give a symbolic solution of the arising optimization problem for various subclasses. This improves the performance of the resulting algorithm considerably.
KeywordsMultigrid Method Symbolic Method Sequential Quadratic Programming Algorithm Positive Linear Combination Cylindrical Algebraic Decomposition
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- B. Buchberger, An algorithm for finding a basis for the residue class ring of a zero-dimensional polynomial ideal, Ph.D. thesis, Universitat Innsbruck, Institut fur Mathematik, 1965, German.Google Scholar
- —, Gröbner bases: An algorithmic method in polynomial ideal theory, Recent Trends in Multidimensional Systems Theory (N. K. Bose, ed.), D. Riedel Publ. Comp., 1985.Google Scholar
- G. E. Collins, Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition, Lecture Notes In Computer Science, Springer, 1975, Vol. 33, pp. 134–183.Google Scholar
- W. Hackbusch, Multigrid methods and application, Springer Verlag, Berlin, Heidelberg, New York, 1985.Google Scholar
- H. Hong, Improvements in cad-based quantifier elimination, Ph.D. thesis, The Ohio State University, 1990.Google Scholar
- M. Jung, U. Langer, A. Meyer, W. Queck, and M. Schneider, Multigrid preconditioners and their application, Proceedings of the 3rd GDR Multigrid Seminar held at Biesenthal, Karl-Weierstraß-Institut für Mathematik, May 1989, pp. 11–52.Google Scholar
- F. Winkler, Polynomial algorithms in computer algebra, Springer, 1996.Google Scholar