Gauss quadrature for quasi-definite linear functionals

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10360928" target="_blank" >RIV/00216208:11320/17:10360928 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1093/imanum/drw032" target="_blank" >http://dx.doi.org/10.1093/imanum/drw032</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/imanum/drw032" target="_blank" >10.1093/imanum/drw032</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Gauss quadrature for quasi-definite linear functionals

Popis výsledku v původním jazyce

Gauss quadrature can be formulated as a method for approximating positive-definite linear functionals. Its mathematical context is extremely rich, with orthogonal polynomials, continued fractions and Padé approximation on one (functional analytic or approximation theory) side, and the method of moments,(real) Jacobi matrices, spectral decompositions and the Lanczos method on the other (algebraic) side. The quadrature concept can therefore be developed in many different ways. After a brief review of the mathematical interconnections in the positive-definite case, this paper will investigate the question of a meaningful generalization of Gauss quadrature for approximation of linear functionals that are not positive definite. For that purpose we use the algebraic approach, and, in order to build up the main ideas, recall the existing results presented in literature. Along the way we refer to the associated results expressed through the language of rational approximations. As the main result, we present the form of generalized Gauss quadrature and prove that the quasi-definiteness of the underlying linear functional represents a necessary and sufficient condition for its existence.

Název v anglickém jazyce

Gauss quadrature for quasi-definite linear functionals

Popis výsledku anglicky

Gauss quadrature can be formulated as a method for approximating positive-definite linear functionals. Its mathematical context is extremely rich, with orthogonal polynomials, continued fractions and Padé approximation on one (functional analytic or approximation theory) side, and the method of moments,(real) Jacobi matrices, spectral decompositions and the Lanczos method on the other (algebraic) side. The quadrature concept can therefore be developed in many different ways. After a brief review of the mathematical interconnections in the positive-definite case, this paper will investigate the question of a meaningful generalization of Gauss quadrature for approximation of linear functionals that are not positive definite. For that purpose we use the algebraic approach, and, in order to build up the main ideas, recall the existing results presented in literature. Along the way we refer to the associated results expressed through the language of rational approximations. As the main result, we present the form of generalized Gauss quadrature and prove that the quasi-definiteness of the underlying linear functional represents a necessary and sufficient condition for its existence.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/LL1202" target="_blank" >LL1202: Materiály s implicitními konstitutivními vztahy: Od teorie přes redukci modelů k efektivním numerickým metodám</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

IMA Journal of Numerical Analysis

ISSN

0272-4979

e-ISSN

—

Svazek periodika

37

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

28

Strana od-do

1468-1495

Kód UT WoS článku

000405416900015

EID výsledku v databázi Scopus

2-s2.0-85027050632