The alternate direction iterative methods for generalized saddle point systems

Shuanghua Luo,Cheng-Yi Zhang,Angang Cui

doi:10.1186/s13660-019-2235-z

Shuanghua Luo, Cheng-Yi Zhang + Show 1 more

Open Access

https://doi.org/10.1186/s13660-019-2235-z

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Abstract

The paper studies two splitting forms of generalized saddle point matrix to derive two alternate direction iterative schemes for generalized saddle point systems. Some convergence results are established for these two alternate direction iterative methods. Meanwhile, a numerical example is given to show that the proposed alternate direction iterative methods are much more effective and efficient than the existing one.

Highlights

0 –B2 0 which is called dimensional splitting of A , and proposed the following alternate direction iterative method:
We propose two types of alternate direction iterative methods: one is that on base of the dimensional splitting (3) the quantitative matrix αI is replaced by two nonnegative diagonal matrices D1 and D2 to form a new alternate direction iterative scheme; another is to propose a new splitting of A, i.e., A = B1 + B2, (6)
Some convergence results are established for the two alternate direction iterative schemes and a numerical example is given to show that the proposed ADI methods are much more effective and efficient than the existing one

Summary

Introduction

0 –B2 0 which is called dimensional splitting of A , and proposed the following alternate direction iterative method: –B1 0 0 and apply the two nonnegative diagonal matrices D1 and D2 to the new splitting such that another new alternate direction iterative scheme is obtained. Some convergence results are established for the two alternate direction iterative schemes and a numerical example is given to show that the proposed ADI methods are much more effective and efficient than the existing one.

Results

Conclusion