Inhomogeneous Eigenvalue Problems  

作　　者：刘颖 蔡大用 

出　　处：《Tsinghua Science and Technology》1998年第4期1260-1264,共5页清华大学学报（自然科学版（英文版）

摘　　要：In this paper, the inhomogeneous eigenvalue problems were studied:give A∈C n×n and b ∈C\+n(b≠0), determine a vector x with x Hx=1 and a scalar λ such that (A-λI)x=b.Here λ is called the inhomogeneous eigenvalue of A with respect to b. Using matrix analytic methods, an equivalent definition of inhomogeneous eigenvalue is given, which is concerned in the pseudospectra of matrix A. Then the necessary and sufficient condition for the existence of real inhomogeneous eigenvalues is discussed. Finally the curve tracing method for the inhomogeneous eigenvalues is investigated, numerical examples are given.In this paper, the inhomogeneous eigenvalue problems were studied:give A∈C n×n and b ∈C\+n(b≠0), determine a vector x with x Hx=1 and a scalar λ such that (A-λI)x=b.Here λ is called the inhomogeneous eigenvalue of A with respect to b. Using matrix analytic methods, an equivalent definition of inhomogeneous eigenvalue is given, which is concerned in the pseudospectra of matrix A. Then the necessary and sufficient condition for the existence of real inhomogeneous eigenvalues is discussed. Finally the curve tracing method for the inhomogeneous eigenvalues is investigated, numerical examples are given.

关 键 词：INHOMOGENEOUS EIGENVALUE PSEUDOSPECTRA 

分 类 号：O151.21[理学—数学]