Matrix Inverse Eigenvalue Problem

Recent years,we pay more attention on the inverse eigenvalue problemof matrix,and we are frequently encountered the inverse problem bothin learning and living.The inverse eigenvalue problem of matrix is stud-ied in many fields,mainly from structural design and analysis!systemparameter identification!automation control!dispersed mathematicalphysical inverse problem!mechanical system simulation!molecular spec-troscopy!geophysics and particle physics and so on.In recent decades,people are tend to discuss the inverse eigenvalue prob-lem of matrix which has special structure,the more representative is theinverse eigenvalue problem of Jacobi matrix.The inverse eigenvalue prob-lem of Jacobi matrix is mainly from compound pendulum,spring particlevibration system and Sturm ?? Liouvile actual problems. Some expertsand scholars research the methods on the inverse eigenvalue problem ofJacobi matrix include: component method,singular value decompositionand iterative method.The most universal method in study the inverse eigenvalue problem ofJacobi matrix is component method,this method is easy to understand andcarry out.In this paper,I discuss two kinds of inverse eigenvalue problemof Jacobi matrix with the component method:question.is to construct aJacobi matrix by the five characteristics,question /is a kind of generalizedinverse eigenvalue problem of Jacobi matrix.Discuss the problem in thenecessary and suffcient condition of the only solution of the questions,theexpression of the solution and the arithmetic,give the expression of thesolution and the arithmetic in the last.