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Mathematical Problems in Engineering
Volume 2017, Article ID 1729287, 10 pages
Research Article

Accurate and Efficient Evaluation of Chebyshev Tensor Product Surface

1School of Science, National University of Defense Technology, Changsha, China
2College of Computer, National University of Defense Technology, Changsha, China
3State Key Laboratory of Astronautic Dynamics, Xi’an, China

Correspondence should be addressed to Hao Jiang; nc.ude.tdun@gnaijoah

Received 10 March 2017; Accepted 3 July 2017; Published 27 September 2017

Academic Editor: Elisa Francomano

Copyright © 2017 Keshan He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A Chebyshev tensor product surface is widely used in image analysis and numerical approximation. This article illustrates an accurate evaluation for the surface in form of Chebyshev tensor product. This algorithm is based on the application of error-free transformations to improve the traditional Clenshaw Chebyshev tensor product algorithm. Our error analysis shows that the error bound is in contrast to classic scheme , where is working precision and is a condition number of bivariate polynomial , which means that the accuracy of the computed result is similar to that produced by classical approach with twice working precision. Numerical experiments verify that the proposed algorithm is stable and efficient.