关于实对称矩阵束联立特征值问题

ON THE JOINT EIGENVALUE PROBLEM OF MATRICES

讨论由多参数Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｅ问题离散得到的代数联立特征值问题．首先分析了联立谱的局部性质，然后基于Ｒａｙｌｅｉｇｈ商理论给出一种求解方案，最后研究扰动理论，建立了Ｇｅｒｓｃｈｇｏｒｉｎ圆盘理论、Ｂａｕｅｒ－Ｆｉｋｅ型定理、Ｗｉｅｌａｎｄｔ－Ｈｏｆｆｍａｎ型定理。

The authors deal with the joint eigenvalue problem of matrices resulted from the discretion of multiparameter Sturm Liouville problem. Firstly, the local behavior of the joint spectrum of matrices is investigated, then an algorithm based on Rayeigh quotient theory is proposed, Finally, several perturbation theorems are proved.