On preconditioned Uzawa methods and SOR methods for saddle-point problems
نویسنده
چکیده
This paper studies convergence analysis of a preconditioned inexact Uzawa method for nondi erentiable saddle-point problems. The SOR-Newton method and the SOR-BFGS method are special cases of this method. We relax the Bramble– Pasciak–Vassilev condition on preconditioners for convergence of the inexact Uzawa method for linear saddle-point problems. The relaxed condition is used to determine the relaxation parameters in the SOR–Newton method and the SOR– BFGS method. Furthermore, we study global convergence of the multistep inexact Uzawa method for nondi erentiable saddle-point problems. c © 1998 Elsevier Science B.V. All rights reserved. AMS classi cation: 65H10
منابع مشابه
Optimization of the parameterized Uzawa preconditioners for saddle point matrices
The parameterized Uzawa preconditioners for saddle point problems are studied in this paper. The eigenvalues of the preconditioned matrix are located in (0, 2) by choosing the suitable parameters. Furthermore, we give two strategies to optimize the rate of convergence by finding the suitable values of parameters. Numerical computations show that the parameterized Uzawa preconditioners can lead ...
متن کاملFast One-Parameter Variant of Preconditioned Uzawa Method with a Scaled Preconditioner for Saddle Point Problems
In this paper, we propose a fast one-parameter variant of preconditioned Uzawa (OVPU) method with a scaled preconditioner for solving the saddle point problems, and then we present its convergence region and a formula for finding its optimal parameter. Also performance of the proposed OVPU method with a scaled preconditioner is compared with the existing one or two parameter iterative methods w...
متن کاملOn generalized preconditioned Hermitian and skew-Hermitian splitting methods for saddle point problems
In this paper, we study the iterative algorithms for saddle point problems(SPP). Bai, Golub and Pan recently studied a class of preconditioned Hermitian and skew-Hermitian splitting methods(PHSS). By further accelerating it with another parameters, using the Hermitian/skew-Hermitian splitting iteration technique we present the generalized preconditioned Hermitian and skew-Hermitian splitting me...
متن کاملAccelerating the Uzawa Algorithm
The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixedpoint iteration, we explore the use of Anderson acceleration (also knownas Anderson mixing) to improve the convergence. We compare the performance of the preconditioned Uzawa algorithm with and without acceleratio...
متن کاملNonlinear Inexact Uzawa Algorithms for Linear and Nonlinear Saddle-point Problems
This paper proposes some nonlinear Uzawa methods for solving linear and nonlinear saddle-point problems. A nonlinear inexact Uzawa algorithm is first introduced for linear saddlepoint problems. Two different PCG techniques are allowed in the inner and outer iterations of the algorithm. This algorithm is then extended for a class of nonlinear saddle-point problems arising from some convex optimi...
متن کامل