Based on the theory of reyleigh minimum , the minimum of energy function of neural network was mapped to the eigenvector that was mapped to the minimal eigenvalue of the generalized eigenvalue problem , by which the precise solution of minimal eigenvalue was gained while the neural network moving to the minimum of energy function 本文應用reyleigh極小值原理，將神經網絡的能量函數的極小點對應于廣義特征值問題的極小特征值所對應的特征向量，在神經網絡向著能量函數極小點運動的同時得到了極小特征向量的精確解答。
The second localization method , called esprit - corr needs no pairing , which is based on the joint estimation of bearing and time - delay . by construct a correlation matrix different from conventional esprit , the method estimates bearings using the general eigenvalues , estimates time - delays using corresponding general eigenvectors , and the parameters in two dimensions are paired automatically 這是一種方位?時延聯合估計的方法它通過構造與常規esprit不同的相關矩陣，用廣義特征值估計多目標的方位，而用廣義特征矢量估計多目標的時延(距離) ，同時方位和時延參數可自動配對。
It plays a very important role in many application , according to the point of mathematics point , its mostly application originate from equations of mathematical physics , difference equations , markov process , and so on , its purpose is to solve the problems of solid , fluid , electromagnetic , microscopic particles , system control , and etc . in practical science research and engineer applications , such as , architecture project , research of aeronautics and astronautics , bioscience , computing physics and oil reconnoiter , many large scale generalized eigenvalue problems need to be solved 它在很多應用中扮演非常重要的角色，從數學角度來看，矩陣特征值問題的應用大多來自數學物理方程、差分方程、 markov過程等。目的是為了計算固體、流體、電磁、微觀粒子、系統控制等重大問題。在實際的科學研究與工程應用中，比如在建筑工程、航空航天研究、生物科學、計算物理以及石油勘探中，都要涉及到大規模矩陣廣義特征值問題的計算。
Following from the results of sensitivity analysis of standard eigenvalue problems , the differentiability of semisimple multiple eigenvalues of nonsymmetric generalized eigenvalue problems is proved , and the derivatives of semisimple multiple eigenvalues and the series expansions of the corresponding eigenvectors are obtained 摘要以標準特征值問題靈敏度分析的有關結論為基礎，證明了單參數非對稱廣義特征值問題半單重特征值的可微性，給出了特征值導數的表達式和特征向量的級數展開式。
The main productions are summarized as follows : ( 1 ) the symmetric - definite tridiagonal generalized eigenvalue problems i ) a divide - and - conquer algorithm is proposed . the original problem is divided into two subproblems , and the sum of the subproblem ' s scales is equal to the original problem ' s scale 本文的主要研究成果概括如下： ( 1 )關于實對稱定三對角矩陣廣義特征值問題? )提出了一種基于等規模矩陣劃分策略的分治算法，子問題的規模之和等于原問題的規模。
