TY - JOUR
T1 - Submatrix Constrained Inverse Eigenvalue Problem involving Generalised Centrohermitian Matrices in Vibrating Structural Model Correction
AU - Wei-Ru Xu & Guo-Liang Chen
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 42
EP - 59
PY - 2018
DA - 2018/02
SN - 6
DO - http://doi.org/10.4208/eajam.200715.181115a
UR - https://global-sci.org/intro/article_detail/eajam/10772.html
KW - Left and right inverse eigenvalue problem, optimal approximation problem, generalised centrohermitian matrix, submatrix constraint.
AB - <p style="text-align: justify;">Generalised centrohermitian and skew-centrohermitian matrices arise in a
variety of applications in different fields. Based on the vibrating structure equation $M$<span style="text-align: justify;">$\ddot{x}$</span><span style="font-family:等线"><span style="font-size: 19px;"></span></span>+$(D+G)$$\dot{x}$+$Kx$=$f(t)$ where $M$, $D$, $G$, $K$ are given matrices with appropriate sizes
and x is a column vector, we design a new vibrating structure mode. This mode can be
discretised as the left and right inverse eigenvalue problem of a certain structured matrix.
When the structured matrix is generalised centrohermitian, we discuss its left and
right inverse eigenvalue problem with a submatrix constraint, and then get necessary
and sufficient conditions such that the problem is solvable. A general representation of
the solutions is presented, and an analytical expression for the solution of the optimal
approximation problem in the Frobenius norm is obtained. Finally, the corresponding
algorithm to compute the unique optimal approximate solution is presented, and we
provide an illustrative numerical example.</p>