Stabilization of Stochastic Iterative Methods for Singular and Nearly Singular Linear Systems
نویسندگان
چکیده
منابع مشابه
Stabilization of Stochastic Iterative Methods for Singular and Nearly Singular Linear Systems
We consider linear systems of equations, Ax = b, with an emphasis on the case where A is singular. Under certain conditions, necessary as well as sufficient, linear deterministic iterative methods generate sequences {xk} that converge to a solution, as long as there exists at least one solution. This convergence property can be impaired when these methods are implemented with stochastic simulat...
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In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...
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In this paper, we discuss semiconvergence of the alternating iterative methods for solving singular systems. The semiconvergence theories for the alternating methods are established when the coefficient matrix is a singular matrix. Furthermore, the corresponding comparison theorems are obtained. Keywords—Alternating iterative method; Semiconvergence; Singular matrix.
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The purpose of this paper is to develop a convergence theory for multigrid methods applied to nearly singular linear elliptic partial differential equations of the type produced from a positive definite system by a shift with the identity. One of the important aspects of this theory is that it allows such shifts to vary anywhere in the multigrid scheme, enabling its application to a wider class...
متن کاملsingular constrained linear systems
in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...
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ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2014
ISSN: 0364-765X,1526-5471
DOI: 10.1287/moor.2013.0596