Abstract:

In this paper,we give a conjugate gradient iterative algorithm for Hermitian solutions of matrix equations under submatrix constraints.First,we transform the equations into two lower-order equations,then we construct a gradient iterative algorithm by conjugate gradients for lower-order equations to obtain the solutions and the optimal approximation of the matrix equations.Finally some numerical examples are given to verify the effectiveness of this method.

Key words: Submatrix constraint, Hermitian solution, Conjugate gradient iterative, Optimal approximation