Winkler, J.R. and Yang, N. (2014) A structure-preserving matrix method for the deconvolution of two Bernstein basis polynomials. Computer Aided Geometric Design, 31 (6). 317 - 328. ISSN 0167-8396
Abstract
This paper describes the application of a structure-preserving matrix method to the deconvolution of two Bernstein basis polynomials. Specifically, the deconvolution View the MathML sourcehˆ/fˆ yields a polynomial View the MathML sourcegˆ provided the exact polynomial View the MathML sourcefˆ is a divisor of the exact polynomial View the MathML sourcehˆ and all computations are performed symbolically. In practical situations, however, inexact forms, h and f of, respectively, View the MathML sourcehˆ and View the MathML sourcefˆ are specified, in which case g=h/fg=h/f is a rational function and not a polynomial. The simplest method to calculate the coefficients of g is the least squares minimisation of an over-determined system of linear equations in which the coefficient matrix is Tœplitz, but the solution is a polynomial approximation of a rational function. It is shown in this paper that an improved result for g is obtained when the Tœplitz structure of the coefficient matrix is preserved, that is, a structure-preserving matrix method is used. In particular, this method guarantees that a polynomial solution to the deconvolution h/fh/f is obtained, and thus an essential property of the theoretically exact solution is retained in the computed solution. Computational examples that show the improvement in the solution obtained from the structure-preserving matrix method with respect to the least squares solution are presented.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2014 Elsevier. This is an author produced version of a paper subsequently published in Computer Aided Geometric Design. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | Polynomial deconvolution; Bernstein basis polynomials; Structure-preserving matrix methods |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 05 Nov 2015 16:58 |
Last Modified: | 16 Nov 2016 13:42 |
Published Version: | http://dx.doi.org/10.1016/j.cagd.2014.02.009 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.cagd.2014.02.009 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:91525 |