Accurate and efficient evaluation of Chebyshev tensor product surface
type: Item
instance of: scholarly article
title: Accurate and efficient evaluation of Chebyshev tensor product surface
zbMATH Open document ID: 1426.65020
DOI: 10.1155/2017/1729287
author: Keshan He
author: Pei-Bing Du
author: Hao Jiang
author: Chongwen Duan
author: Li-zhi Cheng
author: Hongxia Wang
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: 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 \(u + \mathcal{O} \left(u^2\right) \times \mathtt{cond} \left(P, x, y\right)\) in contrast to classic scheme \(u \times \mathtt{cond}(P, x, y)\), where \(u\) is working precision and \(\mathtt{cond} \left(P, x, y\right)\) is a condition number of bivariate polynomial \(P(x, y)\), 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.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 6971788
describes a project that uses: mctoolbox
describes a project that uses: LBNL
describes a project that uses: XBLAS
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/1729287
OpenAlex ID: W2757442151
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description: scientific article; zbMATH DE number 6971788