一类Jacobi矩阵的逆特征问题  

INVERSE EIGENVALUE PROBLEM FOR A KIND OF JACOBIAN MATRIX

作　　者：李珍珠[1] 

机构地区：[1]湖南零陵学院数学系,永州425000

出　　处：《高等学校计算数学学报》2002年第4期298-306,共9页Numerical Mathematics A Journal of Chinese Universities

摘　　要：This paper considers the following two inverse eigenproblems:( I ) Given α,β,γ∈R and 0-≠x,0≠y,0≠z∈Rn. Find an n×n Jacobian Ma-trix J such that Jx=αx,Jy=βy,Jz=γz, where( I ) Given α,β,γ∈R and 0-≠x,0-≠y,0≠≠z∈Rn. Find an n×n Jacobian Ma-trix J such that Jx=αx,Jy=βy,Jz=γz.Some necessary and sufficient conditions for existence of unique solution toproblem I and the existence of solution to problem I are given. Also explicitexpression of the solution is given.This paper considers the following two inverse eigenproblems? I ) Given R and Find an nxn Jacobian Matrix J such that Jx=ax,Jy=y,Jz=rz, where( II ) Given R and Find an nxn Jacobian Matrix J such that Jx=ax,Jy=y,Jz=rz.Some necessary and sufficient conditions for existence of unique solution to problem I and the existence of solution to problem I are given. Also explicit expression of the solution is given.

关 键 词：JACOBI矩阵 逆特征问题 唯一解 充分必要条件 

分 类 号：O241.6[理学—计算数学]