Least‐squares solutions of matrix inverse problem for bi‐symmetric matrices with a submatrix constraint
Anping Liao, Lei Yuan · Numerical Linear Algebra with Applications · 2007
Abstract An n × n real matrix A = (aij)n × n is called bi‐symmetric matrix if A is both symmetric and per‐symmetric, that is, aij = aji and aij = an+1−1,n+1−i (i, j = 1, 2,..., n). This paper is mainly concerned with finding the least‐squares bi‐symmetric solutions of matrix inverse problem AX = B with a submatrix constraint, where X and B are given matrices of suitable sizes. Moreover, in the corresponding solution set, the analytical expression of the optimal approximation solution to a given matrix A* is derived. A direct method for finding the optimal approximation solution is described in detail, and three numerical examples are provided to show the validity of our algorithm. Copyright © 2007 John Wiley & Sons, Ltd.