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 - <p style="text-align: justify;">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.</p>