A unified derivation of operational matrices for integration in systems analysis

Jiunn Lin Wu, Chin Hsing Chen, Chih Fan Chen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

16 Citations (Scopus)

Abstract

Using the operational matrix of an orthogonal function to perform integration for solving, identifying and optimizing a linear dynamic system has several advantages: (1) the method is computer oriented, thus solving higher order differential equations becomes a matter of dimension increasing; (2) the solution is a multi-resolution type; (3) the answer is convergent, even the size of increment is very large. The traditional method for deriving the operational matrix is very involved and not unified, this paper presents a new unified approach to deriving the operational matrices of orthogonal functions. We apply it first to the derivation of the operational matrices of the square wave group which consist of (i) the block pulse function, (ii) the Walsh function and (iii) the Haar wavelet function, then to the sinusoidal group which includes (i) the discrete Fourier transform, (ii) the discrete cosine transform and (iii) the discrete Hartley transform. Finally, we use the operational matrices to solve a linear differential equation to demonstrate its usefulness.

Original languageEnglish
Title of host publicationProceedings - International Conference on Information Technology
Subtitle of host publicationCoding and Computing, ITCC 2000
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages436-442
Number of pages7
ISBN (Electronic)0769505406, 9780769505404
DOIs
Publication statusPublished - 2000 Jan 1
Event1st International Conference on Information Technology: Coding and Computing, ITCC 2000 - Las Vegas, United States
Duration: 2000 Mar 272000 Mar 29

Publication series

NameProceedings - International Conference on Information Technology: Coding and Computing, ITCC 2000

Other

Other1st International Conference on Information Technology: Coding and Computing, ITCC 2000
CountryUnited States
CityLas Vegas
Period00-03-2700-03-29

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

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    Wu, J. L., Chen, C. H., & Chen, C. F. (2000). A unified derivation of operational matrices for integration in systems analysis. In Proceedings - International Conference on Information Technology: Coding and Computing, ITCC 2000 (pp. 436-442). [844267] (Proceedings - International Conference on Information Technology: Coding and Computing, ITCC 2000). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITCC.2000.844267