Effective solution of a linear system with Chebyshev coefficients

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F09%3A00156807" target="_blank" >RIV/68407700:21230/09:00156807 - isvavai.cz</a>

Alternative codes found

RIV/67985556:_____/09:00326994

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Effective solution of a linear system with Chebyshev coefficients

Original language 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BC - Theory and management systems

OECD FORD branch

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Project

<a href="/en/project/1M0567" target="_blank" >1M0567: Centre for Applied Cybernetics</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2009

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Integral Transforms and Special Functions

ISSN

1065-2469

e-ISSN

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Volume of the periodical

20

Issue of the periodical within the volume

8

Country of publishing house

GB - UNITED KINGDOM

Number of pages

10

Pages from-to

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UT code for WoS article

000267766900004

EID of the result in the Scopus database

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