Efficient preconditioner updates for unsymmetric shifted linear systems
نویسندگان
چکیده
منابع مشابه
Efficient Preconditioner Updates for Shifted Linear Systems
We present a new technique for building effective and low cost preconditioners for sequences of shifted linear systems (A + αI)xα = b, where A is symmetric positive definite and α > 0. This technique updates a preconditioner for A, available in the form of an LDLT factorization, by modifying only the nonzero entries of the L factor in such a way that the resulting preconditioner mimics the diag...
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We present an extension of an update technique for preconditioners for sequences of non-symmetric linear systems that was proposed in [5]. In addition, we describe an idea to improve the implementation of the update technique. We demonstrate the superiority of the new approaches in numerical experiments with a model problem.
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When the computation of efficient preconditioners for individual linear systems of a sequence is expensive, significant reduction of costs can be achieved by updating previous preconditioners. For large and sparse systems, this has been done, among others, by recycling subspaces when using a Krylov subspace method [3], by means of small rank updates when applying Quasi-Newton methods [2] or wit...
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We present two new ways of preconditioning sequences of nonsymmetric linear systems in the special case where the implementation is matrix-free. Both approaches are fully algebraic, they are based on the general updates of incomplete LU decompositions recently introduced in [1], and they may be directly embedded into nonlinear algebraic solvers. The first of the approaches uses a new model of p...
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Newton-Krylov methods, combination of Newton-like methods and Krylov subspace methods for solving the Newton equations, often need adequate preconditioning in order to be successful. Approximations of the Jacobian matrices are required to form preconditioners and this step is very often the dominant cost of Newton-Krylov methods. Therefore, working with preconditioners destroys in principle the...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2014
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2014.03.005