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 inhomogeneou...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.展开更多
基金Supported by the National Natural Science Foundation of China(61473148)the Natural Science Foundation of Jiangsu Province of China(BK20141408)the Fundamental Research Funds for the Central Universities(NZ2014101)
文摘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.
