An algorithm with m-step residual history for solving linear equations: Data interpolation by a multi-shape-factors RBF

We expand the current descent direction in terms of the current residual vector and the previous m-step residual vectors to solve n-dimensional linear equations. The m  +1 expansion coefficients with m≪nm≪n are determined explicitly through the solutions of two optimization problems, such that the resulting double optimal m-step algorithm (DOMSA) in the present paper is very time saving. The DOMSA is proven absolutely convergent step-by-step, and the estimations of residual errors are provided. We propose a new concept of multi-shape factors used in the RBF data interpolation, whose linear equations can be effectively solved by the DOMSA.