单切矩阵Nevanlinna-Pick插值问题  

ON SINGLE TANGENTIAL MATRIX NEVANLINNA-PICK INTERPOLATION PROBLEM

作　　者：金巴[1] 胡永建[1] 

机构地区：[1]北京师范大学数学科学学院,北京100875

出　　处：《北京师范大学学报（自然科学版）》2005年第5期469-472,共4页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10271018)

摘　　要：证明了单切矩阵Nevanlinna-Pick插值问题的Pick矩阵合同等价于一个块Toeplitz矩阵.利用这个结果,将求解一个单切矩阵Nevanlinna-Pick插值问题转化求解某个截断的三角矩阵值矩量问题.This paper proves that the Pick matrix determined by the interpolation data of a single tangential matrix Nevanlinna-Pick interpolation problem is congruent and equivalent to a block Toeplitz matrix. On basis of this result, the solution of a single tangential matrix Nevanlinna-Pick interpolation problem is reduced to the solution of a certain truncated matrix trigonometric mnment problem.

关 键 词：单切矩阵Nevanlinna-Pick插值 Pick矩阵 块Toeplitz矩阵 Vandermonde型矩阵 三角矩阵值矩量问题 

分 类 号：O241.3[理学—计算数学]