矩阵特征值反问题的若干进展

给出矩阵特征值反问题若干进展的一个概述。涉及的专题包括含参数的特征值反问题．Ｊａｃｏｂｉ矩阵和实对称带状矩阵特征值反问题和线性（谱）约束下矩阵（束）逼近问题。这些问题出现在各种应用领域，如粒子物理的核光谱光、结构设计、振动反问题、Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｌｅ反问题和 数学物理反问题的离菜化以及结构动力模型的校正。最近２０年，对这些问题的提法逐渐完善，解的慧生和数值方面已取得了许多重要进展。本文评

Some Developments on the Inverse Eigenvalue Problems for Matrices

A comprehensive survey of some developments regarding the inverse eigenvalue problems for matrices is given. Specific topics include: the inverse eigenvalue problems for contained parameters,the inverse eigenvalue problems for Jacobi and symetric banded matrices, and matrix (pencil) approximation under linear (spectral) restriction. These problems arise in various areas of applications, including nuclear spectroscopy in particle physics, structural design, inverse vibration problems, discretization of the inverse sturmLiouville problems and the inverse problems in mathematical physics,as well as correction of structural dynamic model. The formulation for these problems has been perfected gradually,and there have been important advances in the existence of a solution and the numerical methods of these problems in the last 20 years. Both theoretical results and numerical methods for these problems are reviewed.