Newton additive and multiplicative Schwarz iterative methods
نویسندگان
چکیده
منابع مشابه
Newton Additive and Multiplicative Schwarz Iterative Methods
Convergence properties are presented for Newton additive and multiplicative Schwarz iterative methods for the solution of nonlinear systems in several variables. These methods consist of approximate solutions of the linear Newton step using either additive or multiplicative Schwarz iterations, where overlap between subdomains can be used. Restricted versions of these methods are also considered...
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We consider the solution of the algebraic system of equations which result from the dis-cretization of elliptic equations. A class of multilevel algorithms are studied using the additive Schwarz framework. We establish that, in the general case, the condition number of the iterative operator grows at most linearly with the number of levels. The bound is independent of the mesh sizes and the num...
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In recent years, an algebraic framework was introduced for the analysis of convergence of Schwarz methods for the solution of linear systems of the form Ax = b. Within this framework, additive and multiplicative Schwarz were shown to converge when the coefficient matrix A is a nonsingular M -matrix, or a symmetric positive definite matrix. In this paper, these results are extended to the case o...
متن کاملAsynchronous Weighted Additive Schwarz Methods
A class of asynchronous Schwarz methods for the parallel solution of nonsingular linear systems of the form Ax = f is investigated. This class includes, in particular, an asynchronous algebraic Schwarz method as well as asynchronous multisplitting. Theorems are obtained demonstrating convergence for the cases when A 1 is nonnegative and when A is an H-matrix. The results shown are for both the ...
متن کاملAn Algebraic Convergence Theory for Restricted Additive and Multiplicative Schwarz Methods
In this contribution we use the algebraic representation recently developed for the classical additive and multiplicative Schwarz methods in [FS99, BFNS01] to analyze the restrictive additive Schwarz (RAS) and restrictive multiplicative Schwarz (RMS) methods; see [CS96, CFS98, CS99, QV99]. RAS was introduced in [CS99] as an efficient alternative to the classical additive Schwarz preconditioner....
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ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 2007
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/drm015