Solving composite sum of powers via Padé approximation and orthogonal polynomials with application to optimal PWM problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F14%3A00217660" target="_blank" >RIV/68407700:21230/14:00217660 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.amc.2014.03.081" target="_blank" >http://dx.doi.org/10.1016/j.amc.2014.03.081</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.amc.2014.03.081" target="_blank" >10.1016/j.amc.2014.03.081</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Solving composite sum of powers via Padé approximation and orthogonal polynomials with application to optimal PWM problem

Popis výsledku v původním jazyce

This paper presents methods for solving the polynomial system sum_{j=1}^k x_j^i - sum_{j=k+1}^n x_j^i = p_i, i = 1,2,...,n, which is called the composite sum of powers. It is shown that these polynomial equation can be reduced to a single-variable polynomial equations by exploiting the modified Newton s identities. In this paper we generalize this identity and solve it via Padé approximation theory and the related theory of formal orthogonal polynomials (FOPs). Because the solution forms the roots of FOPs we present several interesting computational procedures, such as the use of three-term reccurence formulas, determinantal formulations and the computation of the eigenvalues of tridiagonal matrices. The computation of this special polynomial system arise in practical engineering task of solving optimal odd symmetry single-phase pulse-width modulated (PWM) problem.

Název v anglickém jazyce

Solving composite sum of powers via Padé approximation and orthogonal polynomials with application to optimal PWM problem

Popis výsledku anglicky

This paper presents methods for solving the polynomial system sum_{j=1}^k x_j^i - sum_{j=k+1}^n x_j^i = p_i, i = 1,2,...,n, which is called the composite sum of powers. It is shown that these polynomial equation can be reduced to a single-variable polynomial equations by exploiting the modified Newton s identities. In this paper we generalize this identity and solve it via Padé approximation theory and the related theory of formal orthogonal polynomials (FOPs). Because the solution forms the roots of FOPs we present several interesting computational procedures, such as the use of three-term reccurence formulas, determinantal formulations and the computation of the eigenvalues of tridiagonal matrices. The computation of this special polynomial system arise in practical engineering task of solving optimal odd symmetry single-phase pulse-width modulated (PWM) problem.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BC - Teorie a systémy řízení

OECD FORD obor

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Projekt

<a href="/cs/project/GPP103%2F10%2FP323" target="_blank" >GPP103/10/P323: Efektivní metody pro optimální PWM problém</a><br>

Návaznosti

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

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Applied Mathematics and Computation

ISSN

0096-3003

e-ISSN

—

Svazek periodika

236

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

593-605

Kód UT WoS článku

000335899200054

EID výsledku v databázi Scopus

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