Communications in Information and Systems

Volume 17 (2017)

Number 1

The Chebyshev accelerating method for progressive iterative approximation

Pages: 25 – 43

DOI: http://dx.doi.org/10.4310/CIS.2017.v17.n1.a2

Authors

Chengzhi Liu (School of Mathematics and Statistics, Central South University, Changsha, China; and College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi, China)

Xuli Han (School of Mathematics and Statistics, Central South University, Changsha, China)

Juncheng Li (College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi, China)

Abstract

This paper proposes a new accelerating method for the progressive iterative approximation by using normalized totally positive bases. We prove that the method achieves an order-of-magnitude improvement compared to the weighted progressive iterative approximation. Moreover, we have shown that the well-known weighted progressive iterative approximation is a special application of the proposed method. The convergence is also analysed for all normalized totally positive bases. At the end, some numerical examples are given to illustrate the efficiency of the proposed method.

Full Text (PDF format)

Research supported by the National Natural Science Foundation of China (Grants No. 11771453) and Hunan Provincial Natural Science Foundation of China (Grants No. 2017JJ3124).