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Applied Numerical Mathematics, 2004
This presentation is intended to review the state-of-the-art of iterative methods for solving large sparse linear systems such as arising in finite difference and finite element approximations of boundary value problems. However, in order to keep this review within reasonable bounds, we only review those methods for which an algebraic analysis has been
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This presentation is intended to review the state-of-the-art of iterative methods for solving large sparse linear systems such as arising in finite difference and finite element approximations of boundary value problems. However, in order to keep this review within reasonable bounds, we only review those methods for which an algebraic analysis has been
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Iterative Substructuring Methods
2004We shall consider the equation $$ x^1 = x^0 - A^{ - 1} (Ax^0 - f) = A^{ - 1} f = x. $$ (3.1) where A: V → V is a symmetric positive definite (s.p.d.) operator with respect to the inner product (·,·) on the finite dimensional vector space V, dim V = N. Let B: V → V be another s.p.d. operator.
Gabriel Wittum, Boris N. Khoromskij
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1989
In this chapter we study implicit two-level iterative methods whose operators B correspond to triangular matrices. In Section 1 we look at the Gauss-Seidel method and formulate sufficient conditions for its convergence. In Section 2, the successive over-relaxation method is investigated.
Evgenii S. Nikolaev +1 more
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In this chapter we study implicit two-level iterative methods whose operators B correspond to triangular matrices. In Section 1 we look at the Gauss-Seidel method and formulate sufficient conditions for its convergence. In Section 2, the successive over-relaxation method is investigated.
Evgenii S. Nikolaev +1 more
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1972
One of the problems which arise from the increasing use of multiprocessing is the efficient utilization of all the processors. If the solution of a problem requires T units of time when only one processor is used, it is hoped that using k processor will require only T/k units of time.
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One of the problems which arise from the increasing use of multiprocessing is the efficient utilization of all the processors. If the solution of a problem requires T units of time when only one processor is used, it is hoped that using k processor will require only T/k units of time.
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Iterative Substructing Methods
1998In the last two chapters, we focus on parallel computation for the combinations given in this book. The combined algorithms can be easily implemented into parallel by the iterative substructing methods, based on the new imbedding techniques provided in this chapter.
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