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Spectral problems of several structured matrices

Abstract

众所周知,在工程计算和实际应用中有许多问题最终都归结为矩阵计算问题,而且不同的应用会导出一些具有特殊结构的矩阵计算.最常见的一些结构矩阵有Toep-litz矩阵[aij][a_{i-j}],Hankel矩阵[ai+j][a_{i+j}],Toeplitz-plus-Hankel矩阵,Cauchy矩阵[1aibj][\frac{1}{a_i-b_j}]等等.处理与这些结构矩阵有关的矩阵计算问题(例如计算特征值、求解线性方程组等),若矩阵的阶数较小时,通常的经典算法是可行的(例如LU分解算法、QR算法等).然而,在许多实际应用当中,矩阵的阶数nn很大(n106109n\sim10^6-10^9)或某个线性方程组需要多次计算直到得...Many important problems in engineering and applied sciences can be finally reduced to matrixcomputation problems. Moreover, various applications often introduce some special structures into the corresponding matrices. Among classical examples are Toeplitz matrices [aij][a_{i-j}], Hankel matrices [ai+j][a_{i+j}], Toeplitz-plus-Hankel matrices, Cauchy matrices [1aibj][\frac{1}{a_i-b_j}] and others.When we ...学位:理学硕士院系专业:数学科学学院信息与计算数学系_计算数学学号:2005130160

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