Inverse Eigenvalue Problem for Quasi-tridiagonal Matrices
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The inverse eigenvalue problem of quasi-tridiagonal matrices involves reconstruction of quasi-tridiagonal matrices with the given eigenvalues satisfying some properties. In particular, we first analyze the eigenvalue properties from two aspects. On this basis, we investigate the inverse eigenvalue problem of quasi-tridiagonal matrices from the theoretic issue on solvability and the practical issue on computability. Sufficient conditions of existence of solutions of the inverse eigenvalue problem of quasi-tridiagonal matrices concerning solvability are found, and algorithms concerning computability are given with the unitary matrix tool from which we construct matrices. Finally, examples are presented to illustrate the algorithms.
KeywordsQuasi-tridiagonal matrix Eigenvalue Inverse eigenvalue problem
Mathematics Subject Classification65F15 15A18
The research was supported partially by National Natural Science Foundation of China (Grant nos. 10871056 and 10971150).