RESEARCH ARTICLE
The Trapezoidal Method of Steepest-Descent and its Application to Adaptive Filtering
T. J. Moir*
School of Engineering and Advanced Technology, Massey University at Albany, Auckland, New-Zealand
Article Information
Identifiers and Pagination:
Year: 2010Volume: 3
First Page: 1
Last Page: 5
Publisher Id: TOSIGPJ-3-1
DOI: 10.2174/18768253010030100001
Article History:
Received Date: 16/11/2009Revision Received Date: 14/12/2009
Acceptance Date: 31/12/2009
Electronic publication date: 19/1/2010
Collection year: 2010
© 2010 T.J. Moir.
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Abstract
The method of steepest-descent is re-visited in continuous time. It is shown that the continuous time version is a vector differential equation the solution of which is found by integration. Since numerical integration has many forms, we show an alternative to the conventional solution by using a Trapezoidal integration solution. This in turn gives a slightly modified least-mean squares (LMS) algorithm.
Keywords: Steepest-Descent, Least-mean squares (LMS), Adaptive filters.
