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?n m ? 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.
double optimal m-step algorithm multi-shape factors linear equations system double optimal solution residual subspace interpolation by rbf