A new approximate inverse preconditioner based on the Vaidya’s maximum spanning tree for matrix equation AXB = C

Abstract

We propose a new preconditioned global conjugate gradient (PGL-CG) method for the solution of matrix equation AXB = C, where A and B are sparse Stieltjes matrices. The preconditioner is based on the support graph preconditioners. By using Vaidya’s maximum spanning tree precon ditioner and BFS algorithm, we present a new algorithm for computing the approximate inverse preconditioners for matrices A and B and constructing a preconditioner for the matrix equation AXB = C. This preconditioner does not require solving any linear systems and is highly parallelizable. Numerical experiments are given to show the efficiency of the new algorithm on CPU and GPU for the solution of large sparse matrix equation.

Keywords

• krylov subspace methods
• matrix equation
• approximate inverse preconditioner
• global conjugate gradient
• support graph preconditioner
• vaidya's maximum spanning tree preconditioner