About: Effective solution of a linear system with Chebyshev coefficients

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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. 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. (en)
Title	Effective solution of a linear system with Chebyshev coefficients Effective solution of a linear system with Chebyshev coefficients (en)
skos:prefLabel	Effective solution of a linear system with Chebyshev coefficients Effective solution of a linear system with Chebyshev coefficients (en)
skos:notation	RIV/67985556:_____/09:00326994!RIV10-MSM-67985556
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M0567), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika	8
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Šebek, Michael Kujan, Petr
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	312347
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/09:00326994
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	orthogonal Chebyshev polynomials; hypergeometric functions; optimal PWM problem (en)
http://linked.open.../riv/klicoveSlovo	hypergeometric functions optimal PWM problem orthogonal Chebyshev polynomials
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[30996129353C]
http://linked.open...i/riv/nazevZdroje	Integral Transforms and Special Functions
http://linked.open...in/vavai/riv/obor	BC
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Centre for Applied Cybernetics
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	20
http://linked.open...iv/tvurceVysledku	Šebek, Michael Hromčík, M. Kujan, Petr
http://linked.open...ain/vavai/riv/wos	000267766900004
http://linked.open...n/vavai/riv/zamer	Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech
issn	1065-2469
number of pages	30 (xsd:int)

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