Convergence of a Class of Stationary Iterative Methods for Saddle Point Problems
نویسنده
چکیده
A unified convergence result is derived for an entire class of stationary iterative methods for solving equality constrained quadratic programs or saddle point problems. This class is constructed from essentially all possible splittings of the n×n submatrix residing in the (1,1)block of the (n+m)×(n+m) augmented matrix that would generate non-expansive iterations in R. The classic multiplier method and augmented Lagrangian alternating direction method are two special members of this class.
منابع مشابه
Generalized iterative methods for solving double saddle point problem
In this paper, we develop some stationary iterative schemes in block forms for solving double saddle point problem. To this end, we first generalize the Jacobi iterative method and study its convergence under certain condition. Moreover, using a relaxation parameter, the weighted version of the Jacobi method together with its convergence analysis are considered. Furthermore, we extend a method...
متن کاملOn Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory
In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...
متن کاملConvergence Properties of Hermitian and Skew Hermitian Splitting Methods
In this paper we consider the solutions of linear systems of saddle point problems. By using the spectrum of a quadratic matrix polynomial, we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method.
متن کاملRegularized HSS Iteration Method for Saddle - Point Linear Systems
We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspace methods. We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding precondi...
متن کاملRegularized HSS iteration methods for saddle-point linear systems
We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspacemethods.We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding preconditi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010