求Hankel型线性方程组的一种算法  

An Algorithm for Solving Hankel-type Linear Equations

作　　者：杨小锋[1,2] 徐仲[1] 聂玉峰[1] 拓明福[3] 

机构地区：[1]西北工业大学应用数学系,西安710072 [2]西北农林科技大学应用数学系,杨凌712100 [3]空军工程大学理学院,西安710051

出　　处：《工程数学学报》2012年第2期245-252,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11071196);陕西省电子信息系统综合集成重点实验室基金(2011ZD08);西北农林科技大学人才基金(01140403)~~

摘　　要：本文给出了矩阵为Hankel矩阵的充要条件,由此定义了一种新的矩阵—Hankel型矩阵,说明了Hankel矩阵是Hankel型矩阵的特殊情况.为了降低Hankel型线性方程组的计算量和减小这类算法的误差,利用Hankel型矩阵的位移性质,给出了求Hankel型线性方程组的一种算法.矩阵为Hankel矩阵时,该算法与Gohberg-Kailath-Koltracht算法相比计算量相当,但改进了精度;矩阵为一般Hankel型矩阵时,该算法与Cholesky分解算法相比计算量大为减少,极大改进了精度.In this paper,the necessary and suffcient conditions for Hankel matrices are obtained.We define Hankel-type matrices,and illustrate Hankel matrices are special cases of Hankel-type matrices.In order to decrease the computation amount and reduce the error of linear equations of Hankeltype matrix,an algorithm is presented in term of the displacement structure of Hankel-type matrix.Although the computation amount of new algorithm is same roughly as the Gohberg-Kailath-Koltracht algorithm,more accurate in precision for solving linear equations of Hankel matrix.In general,the algorithm is faster than the Cholesky triangular decomposition algorithm and more accurate in precision for solving system of linear equations of some Hankel-type matrices.

关 键 词：HANKEL矩阵 Hankel型矩阵 快速算法 充要条件 

分 类 号：O241.6[理学—计算数学]