<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Petr Kujan</style></author><author><style face="normal" font="default" size="100%">Martin Hromčík</style></author><author><style face="normal" font="default" size="100%">Michael Šebek</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Effective solution of a linear system with Chebyshev coefficients</style></title><secondary-title><style face="normal" font="default" size="100%">Integral Transforms and Special Functions</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">hypergeometric functions</style></keyword><keyword><style  face="normal" font="default" size="100%">linear system</style></keyword><keyword><style  face="normal" font="default" size="100%">optimal PWM problem</style></keyword><keyword><style  face="normal" font="default" size="100%">orthogonal Chebyshev polynomials</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dx.doi.org/10.1080/10652460902727938</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Taylor &amp; Francis</style></publisher><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">619-628</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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 are O(m), and no recursion formula is needed. The linear  system is closely related to the optimal pulse-wide modulation problem.&lt;/p&gt;</style></abstract><issue><style face="normal" font="default" size="100%">8</style></issue></record></records></xml>