Research On The Real Symmetric Matrix Inverse Eigenvalue Problems

The characteristic value of the so-called inverse algebraic eigenvalue problem is that under certain restrict conditions against the question,elements of matrix are determined according to eigenvalue or eigenvector.The practical inverse alebraic eigenvalue problem arose in phisical chemistry in the study of molecular structures.It arises in various areas of application in a lot of filelds,such as dispersed system of physical mathematic,design of vibration system of the structure,correct and control,particle nuclear spectroscopy,linear variable control system and so on.This paper mainly discusses the formulation and the numerical methods of real symmetrical matrix inverse algebraic eigenvalue.This includes normal and generalized inverse eigenvalue problem which includes the additive,multiplicative classical inverse eigenvalue problems as special cases.This paper research the numerical solutions and geiven parital condions,this fourmation on some terms is equivalent to anthor formuation,and it is practical to all conditions g iv ed. As for the numericial mthods we present a method using Newton iteration and LP(Lift-Projection) iteration to slove inverse real symmetric eigenvalue problems.Then wo can choose any starting points,then wo can get good starting value for the purpose of the preconditioning The numerical examples show the method is efficient and available.