TY - JOUR T1 - On Parameterised Quadratic Inverse Eigenvalue Problem AU - Xiang , Meiling AU - Dai , Hua JO - East Asian Journal on Applied Mathematics VL - 1 SP - 185 EP - 200 PY - 2021 DA - 2021/10 SN - 12 DO - http://doi.org/10.4208/eajam.250321.230821 UR - https://global-sci.org/intro/article_detail/eajam/19927.html KW - Quadratic inverse eigenvalue problem, multiparameter eigenvalue problem, smooth $QR$-decomposition, Newton method. AB -

It is shown that if prescribed eigenvalues are distinct, then the parameterised quadratic inverse eigenvalue problem is equivalent to a multiparameter eigenvalue problem. Moreover, a sufficient condition for the problem solvability is established. In order to find approximate solution of this problem, we employ the Newton method based on the smooth $QR$-decomposition with column pivoting and prove its locally quadratic convergence. Numerical examples illustrate the effectiveness of the method.