关于解线性系统的一个有效的贝叶斯迭代方法

An efficient Bayesian iterative method for solving linear systems

中文关键词:  线性系统  矩阵  迭代方法  贝叶斯方法．

英文关键词:linear system  matrix  iterative method  Bayesian perspective.

中文摘要:

      本文考虑了关于解线性系统的统计方法．在简单回顾关于反问题的贝叶斯方法后，本文提出一解一般线性系统的一个有效的新的贝叶斯迭代方法．本文还证明了该方法的收敛性，和考虑了其误差分析等问题．最后，本文给出若干关于该方法的数值实验以支持其有效性，并得到若干有关的结论.

英文摘要:

      This paper concerns with the statistical methods for solving general linear systems. After a brief review of Bayesian perspective for inverse problems, a new and efficient iterative method for general linear systems from a Bayesian perspective is proposed. The convergence of this iterative method is proved, and the corresponding error analysis is studied. Finally, numerical experiments are given to support the efficiency of this iterative method, and some conclusions are obtained.