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

作者：Liu Chein Shan^*

来源：Engineering Analysis with Boundary Elements, 2015, 51: 123-135.

DOI：10.1016/j.enganabound.2014.10.020

• Linear equations system
• Double optimal solution
• Residual subspace
• Double optimal m-step algorithm
• Interpolation by REF
• Multi-shape factors

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 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.

• 出版日期2015-2