A New Preconditioner with Two Variable Relaxation Parameters for Saddle Point Linear Systems with Highly Singular(1,1) Blocks

نویسندگان

  • Yuping Zeng
  • Chenliang Li
چکیده

In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Augmentation Preconditioner for Asymmetric Saddle Point Problems with Singular (1,1) Blocks

Abstract In this paper, an augmentation preconditioner for asymmetric saddle point problems with singular (1,1) blocks is introduced on the base of the recent article by He and Huang [Two augmentation preconditioners for nonsymmetric and indefinite saddle point linear systems with singular (1, 1) blocks, Comput. Math. Appl., 62 (2011) 87-92]. We study the spectral characteristics of the precond...

متن کامل

New Block Triangular Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks

We establish two types of block triangular preconditioners applied to the linear saddle point problems with the singular 1,1 block. These preconditioners are based on the results presented in the paper of Rees and Greif 2007 . We study the spectral characteristics of the preconditioners and show that all eigenvalues of the preconditioned matrices are strongly clustered. The choice of the parame...

متن کامل

Validated Solutions of Saddle Point Linear Systems

We propose a fast verification method for saddle point linear systems where the (1,1) block is singular. The proposed verification method is based on an algebraic analysis of a block diagonal preconditioner and rounding mode controlled computations. Numerical comparison of several verification methods with various block diagonal preconditioners is given.

متن کامل

New Preconditioners with Two Variable Relaxation Parameters for the Discretized Time-Harmonic Maxwell Equations in Mixed Form

We provide new preconditioners with two variable relaxation parameters for the saddle point linear systems arising from finite element discretization of time-harmonic Maxwell equations in mixed form. The new preconditioners are of block-triangular forms and Schur complement-free. They are extensions of the results in Cheng et al., 2009, Grief and Schötzau, 2007, and Huang et al., 2009. Theoreti...

متن کامل

Augmented Lagrangian Techniques for Solving Saddle Point Linear Systems

We perform an algebraic analysis of a generalization of the augmented Lagrangian method for solution of saddle point linear systems. It is shown that in cases where the (1,1) block is singular, specifically semidefinite, a low-rank perturbation that minimizes the condition number of the perturbed matrix while maintaining sparsity is an effective approach. The vectors used for generating the per...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012