Block Iterative Methods for Elliptic and Parabolic Difference Equations

Abstract

Direct iterative methods for solving the linear system $AX = Y$ split A into a difference $M - N$. By viewing N as a weak multiplication operator, we determine the convergence rates of block direct iterative methods for elliptic and parabolic difference equations. The difference equations may arise from very general partial differential equations on general domains in m space dimensions.