On The Solving Of Two Particular Matrix Equation

The paper include two parts.First,we consider the complex matrix equation AXAH= B.Using SVDs,we give the formula of least squares solutions for Hermitian R-(skew) symmetric matrices,then we get the least norm solution by Q-SVD.In the second part,we describe Krylov subspace methods for solving large Sylvester equation AX+XB= C with some structure. The proposed algorithms use Krylov subspaces for which orthogonal bases are generated by the global Lanczos process. This makes the algorithms suitable for the matrix equation. Based on the symmetry and skew-symmetry splitting of the coef-ficient matrix,we get the new method from the FOM method. Numerical experiments and application are done to illustrate the effectiveness of the proposed algorithms compared with the GMRES method.