一类广义Sylvester方程的反对称最小二乘解及其最佳逼近

THE LEAST-SQUARES SKEW-SYMMETRIC SOLUTION AND THE OPTIMAL APPROXIMATION ON A CLASS OF GENERALIZED SYLVESTER EQUATION

本文利用矩阵的奇异值分解(SVD),给出了广义Sylvester矩阵方程AX+YA=C反对称解存在的充分必要条件,导出了其反对称解和反对称最小二乘解的表达式,同时在解集合中得到了对给定矩阵的最佳逼近解.

Using the singular value decomposition (SVD) of the matrix A, this paper obtains the necessary and sufficient conditions for the existence of and the expresssions of the skew-symmetric solutions of the generalized Sylvester matrix equation AX + YA = C, and the least-squares skew-symmetric solution of this equation. In addition, in the solution set of the corresponding problems, the expressions of the optimal approximation solutions are derived for the given marices .