Stationary splitting iterative methods for the matrix equation AXB=C

Abstract

Stationary splitting iterative methods for solving AXB = C are considered in this paper. The main tool to derive our new method is the induced splitting of a given nonsingular matrix A = M − N by a matrix H such that (I − H) −1 exists. Convergence properties of the proposed method are discussed and numerical experiments are presented to illustrate its computational efficiency and the effectiveness of some preconditioned variants. In particular, for certain surface-fitting applications our method is much more efficient than the progressive iterative approximation (PIA), a conventional iterative method often used in computer aided geometric design (CAGD).

On the Convergence of the Randomized Block Kaczmarz Algorithm for Solving a Matrix Equation

“…Such problems arise in many practical applications such as surface fitting in computer-aided geometric design (CAGD), signal and image processing, photogrammetry, etc. ; see, for example, [1][2][3][4] and the large body of literature therein. If AXB = C is consistent, X * = A † CB † is the minimum Frobenius norm solution.…”