一种多项式预处理算法  

A Method about Polynomial Preconditioning Technique

作　　者：刘播[1] 刘凤楠[1] 

机构地区：[1]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2012年第1期11-14,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:J1030101);吉林省自然科学基金(批准号:201115044)

摘　　要：基于二次函数的性质,针对对称正定线性方程组,提出一种多次多项式预处理算法,并证明了该算法能有效改善条件数,提高运算效率.在此基础上,设计一种求方程组近似解的方法,数值实验结果表明了算法的有效性.A method of multiple polynomial preconditioning technique for positive definite symmetric linear equations was proposed based on the nature of the quadratic function.It was proved that the method can make condition number better so as to improve operation efficiency.On the basis,a method of approximate solution of equations was designed,and the theoretical results and numerical results show the effectiveness of the method.

关 键 词：预处理 条件数 多项式预处理 

分 类 号：O241.6[理学—计算数学]