Gauss quadrature for quasi-definite linear functionals

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Gauss quadrature for quasi-definite linear functionals
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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