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Effective solution of a linear system with Chebyshev coefficients
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SYSNO ASEP 0326994 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Effective solution of a linear system with Chebyshev coefficients Title Efektivní řešení lineárního systému pomocí Chebyshevových koeficientů Author(s) Kujan, Petr (UTIA-B) RID
Hromčík, M. (CZ)
Šebek, Michael (UTIA-B) RIDSource Title Integral Transforms and Special Functions - ISSN 1065-2469
Roč. 20, č. 8 (2009), s. 619-628Number of pages 30 s. Publication form www - www Language eng - English Country GB - United Kingdom Keywords orthogonal Chebyshev polynomials ; hypergeometric functions ; optimal PWM problem Subject RIV BC - Control Systems Theory R&D Projects 1M0567 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000267766900004 DOI 10.1080/10652460902727938 Annotation This paper presents an efficient algorithm for a special triangular linear system with Chebyshev coefficients. We present two methods of derivations, the first is based on formulae where the nth power of x is solved as the sum of Chebyshev polynomials and modified for a linear system. The second deduction is more complex and is based on the Gauss–Banachiewicz decomposition for orthogonal polynomials and the theory of hypergeometric functions which are well known in the context of orthogonal polynomials. The proposed procedure involves O(nm) operations only, where n is matrix size of the triangular linear system L and m is number of the nonzero elements of vector b. Memory requirements areO(m), and no recursion formula is needed. The linear system is closely related to the optimal pulse-wide modulation problem. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2010
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