Effective solution of a linear system with Chebyshev coefficients

0326994 - ÚTIA 2010 RIV GB eng J - Journal Article
Kujan, Petr - Hromčík, M. - Šebek, Michael
Effective solution of a linear system with Chebyshev coefficients.
[Efektivní řešení lineárního systému pomocí Chebyshevových koeficientů.]
Integral Transforms and Special Functions. Roč. 20, č. 8 (2009), s. 619-628. ISSN 1065-2469. E-ISSN 1476-8291
R&D Projects: GA MŠMT(CZ) 1M0567
Institutional research plan: CEZ:AV0Z10750506
Keywords : orthogonal Chebyshev polynomials * hypergeometric functions * optimal PWM problem
Subject RIV: BC - Control Systems Theory
Impact factor: 0.756, year: 2009
http://dx.doi.org/10.1080/10652460902727938

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.

Článek prezentuje efektivní algoritmus pro specielní trojúhelnikový lineární systém s Chebyshevovými koeficienty. Předkládáme dvě metody derivací, první je založena na rovnici, kde n-tá mocnica z x je řešena jako suma Chebyshevových polynomů a modifikována pro lineární systém. Druhé odvození je více komplexní a je založeno na Gauss-Banachiewicz dekompozici pro ortogonální polynomy a teorii hypergeometrických funkcí.
Permanent Link: http://hdl.handle.net/11104/0173907