TY - JOUR T1 - General Solutions for a Class of Inverse Quadratic Eigenvalue Problems JO - East Asian Journal on Applied Mathematics VL - 1 SP - 69 EP - 81 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.100413.021013a UR - https://global-sci.org/intro/article_detail/eajam/10822.html KW - Quadratic eigenvalue problem, inverse quadratic eigenvalue problem, partially prescribed spectral information. AB -

Based on various matrix decompositions, we compare different techniques for solving the inverse quadratic eigenvalue problem, where $n×n$ real symmetric matrices $M$, $C$ and $K$ are constructed so that the quadratic pencil $Q(λ) = λ^{2}M+λC+K$ yields good approximations for the given $k$ eigenpairs. We discuss the case where $M$ is positive definite for $1≤ k≤n$, and a general solution to this problem for $n+1≤k≤2n$. The efficiency of our methods is illustrated by some numerical experiments.