| Matrix inverse eigenvalue problems is, under certain constraints, onseeking a matrix with some given eigenvalues and eigenvectors. Matrix inverseeigenvalue problems arise in a remarkable variety of applications. The listincludes but is not limited to molecular spectroscopy,structure analysis, controldesign and so on. The study of it has been became a hot topic in the field ofnumerical algebra in recent years. For the Jacobi matrix, there has alreadyexisted many literatures concerning its inverse eigenvalue problems andgeneralized inverse eigenvalue problems. However, the results on paw formmatrix are still seldom due to its difficulties. Since the paw form matrix is theclaw-conditioning systems control the parameters of the matrix equation, thestudy of the paw form matrix inverse eigenvalue problem and generalizedinverse eigenvalue problem is particularly important.In this thesis, we mainlyconcentrate on those problems of two new paw form matrics. By converting theoriginal problems into solving equations, we can obtain some conditions on theexistence and uniqueness solution with explicit expression. The thesis consistsof four chapters, details are as follows:The first chapter is an introduction. We give some basic knowledge and theexisted results of the home and abroad on the inverse eigenvalue problem aswell as generalized inverse eigenvalue problem, and the basic ideas andinnovation of this paper to elaborate.The second chapter is the main part of this paper. After showing four kindsof paw form matrics, we put forward the problems on them separately and talkabout the uniqueness conditions. To illustrate, two of them has been givenconcrete algorithm and numerical examples.The third chapter mainly discusses a class of generalized inverse eigenvalueproblem on paw form matrix and obtain its explicit expression.The last chapter consider the inverse eigenvalue problem of closed andsemi-closed paw form matrics. A sufficient condition has been given as well astheir proofs. |
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