INTEGRAÇÃO NUMÉRICA SOBRE ESPAÇOS DE DIMENSÃO N â¥1

Favaro, Marielza Jorge

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

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Master's Dissertation

DOI

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

Document

Master's Dissertation

Author

Favaro, Marielza Jorge (Catálogo USP)

Full name

Marielza Jorge Favaro

Institute/School/College

Instituto de Ciências Matemáticas e de Computação

Knowledge Area

Mathematics

Date of Defense

1973-01-06

Published

São Carlos, 1973

Supervisor

Linhares, Odelar Leite (Catálogo USP)

Committee

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

Title in Portuguese

INTEGRAÇÃO NUMÉRICA SOBRE ESPAÇOS DE DIMENSÃO N ≥1

Keywords in Portuguese

Não disponível

Abstract in Portuguese

Não disponível

Title in English

Numerical Integration over Spaces of dimension n ≥ 1

Keywords in English

Not available

Abstract in English

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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Dissertacao_MarielzaJorgeFavaro_1973.pdf (2.18 Mbytes)

Publishing Date

2022-06-22

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