INTEGRAÇÃO NUMÉRICA SOBRE ESPAÇOS DE DIMENSÃO N â¥1

Favaro, Marielza Jorge

doi:10.11606/D.55.1973.tde-22062022-080847

Accueil

Services

Mémoire de Maîtrise

DOI

https://doi.org/10.11606/D.55.1973.tde-22062022-080847

Document

Mémoire de Maîtrise

Auteur

Favaro, Marielza Jorge (Catálogo USP)

Nom complet

Marielza Jorge Favaro

Unité de l'USP

Instituto de Ciências Matemáticas e de Computação

Domain de Connaissance

Mathématiques

Date de Soutenance

1973-01-06

Editeur

São Carlos, 1973

Directeur

Linhares, Odelar Leite (Catálogo USP)

Jury

Linhares, Odelar Leite (Président)
Onuchic, Nelson
Saab, Mario Rameh

Titre en portugais

INTEGRAÇÃO NUMÉRICA SOBRE ESPAÇOS DE DIMENSÃO N ≥1

Mots-clés en portugais

Não disponível

Resumé en portugais

Não disponível

Titre en anglais

Numerical Integration over Spaces of dimension n ≥ 1

Mots-clés en anglais

Not available

Resumé en anglais

The purpose of this work is to discuss methods to calculate approximately multiple integrals. The approximations are of the form ∫ ... ∫ _R_n w(x₁,...,x_n) f(x₁,...,x_n) d_x1l ... d_x_{n ≃ ∑^N_i=1 A_if(v_li,...,v_ni) R_n and are of a certain degree d. Integration formulae for simple regions 'like simplex and complex are presented which generalíze the one dimension Newton-Cotes formulas. Many of the existing generalizations of the Newton-Cotes formulae use a number of base-points N = (n+d) ! / n! d! whereas those discussed use mostly N < (n+d)! / n! d! and are numerically better as analagous results are obtained with less basepoints. Integration formulae using orthogonal polynomials are also .discussed which generalize the one dimension Gauss formulae. The result "of A.H.Stroud [Q] gives a necessary and suficient condition for the common zeros of a set of polynomials in n-variables to be used as basepoints in an integration formula. | The main result of this work is the R. Franke theorem. [id] that has practical interest because: i) the hypothesis are more easely verified than those of A.H.Stroud; ii) the number of orthogonal polynomials and that of base-points is well determined for each chosen n; iii) the number of base-points is always given by N ≤ mⁿ < (n+d)! / n! d! which is numerically more feasible.}

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Date de Publication

2022-06-22

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