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Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/unesp/360685
Title: 
Orthogonality of Two Functions with Weighted Inner Products
Author(s): 
Goriely, Alain
Language: 
eng
Description: 
  • Two functions are orthogonal with respect to a weighted inner product if the integral of the product of the two functions and the weight function is identically zero on the chosen interval. Finding a family of orthogonal functions is important in order to identify a basis for a function space. Once a basis is found, all functions in that particular function space can be expanded with respect to the orthogonal functions. The choice of trigonometric functions sine and cosine lead to Fourier analysis which is a central tool for analyzing periodic signals. Other families of orthogonal functions, such as orthogonal polynomials, find application in numerical techniques such as least-squares approximations, Gauss and related quadrature, iterative methods in linear algebra, the detection of singularities, integral equations, and wavelets in medical diagnostics, but also in optimal control, dynamical systems, gas dynamics, integrable systems, and random matrices. Different examples of orthogonal functions are provided with two choices of weight functions on two different intervals. The functions and their weighted product are displayed together with the signed area. The inner product with the chosen weight is computed to test for orthogonality
  • Componente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática
Issue Date: 
  • 11-Sep-2008
  • 11-Sep-2008
  • 2008
  • 11-Sep-2008
  • 9-Sep-2008
Publisher: 
Wolfram
Keywords: 
  • Approximation Methods
  • Educação Superior::Ciências Exatas e da Terra::Matemática::Análise
Credits: 
This demonstration needs the "MathematicaPlayer.exe" to run. Found in http://objetoseducacionais2.mec.gov.br/handle/mec/4737
Source: 
http://objetoseducacionais2.mec.gov.br/handle/mec/5240
URI: 
http://acervodigital.unesp.br/handle/unesp/360685
Rights: 
Demonstration freeware using Mathematica Player
Type: 
outro
Appears in Collections:MEC - Objetos Educacionais (BIOE) - OE

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