On a General Solution of Partially Described Inverse Quadratic Eigenvalue Problems and Its Applications
نویسندگان
چکیده
In this paper, we consider to solve a general form of real and symmetric n× n matrices M , C, K with M being positive definite for an inverse quadratic eigenvalue problem (IQEP): Q(λ)x ≡ (λ2M + λC +K)x = 0, so that Q(λ) has a partially prescribed subset of k eigenvalues and eigenvectors (k ≤ n). Via appropriate choice of free variables in the general form of IQEP, for k = n: we solve (i) an IQEP with K semi-positive definite, (ii) an IQEP having additionally assigned n eigenvalues, (iii) an IQEP having additionally assigned r eigenpairs (r ≤ √n) under closed complex conjugation; for k < n: we solve (i) a unique monic IQEP with k = n−1 which has an additionally assigned complex conjugate eigenpair, (ii) an IQEP having additionally assigned 2(n−k) complex eigenvalues with nonzero imaginary parts. Some numerical results are given to show the solvability of the above described IQEPs. National Center for Theoretical Sciences Mathematics Division, Hsinchu, 300, Taiwan ([email protected]). Department of Mathematics, National Tsinghua University, Hsinchu, 300, Taiwan ([email protected]). LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, China ([email protected]).
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