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Polynomials data fitting

Grant number: 20/15247-5
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): January 01, 2021
Effective date (End): December 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal researcher:Vanessa Gonçalves Paschoa Ferraz
Grantee:Felipe Ikejiri Hilário
Home Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil

Abstract

When we have a data table $ (x_0, y_0), (x_1, y_1), \ ldots (x_N, y_N) $ the question of how we can find a mathematical function that approximates this data is very common. One possibility is to look for a function that interpolates the data, that is, a function $ p $ that satisfies $ p (x_j) = y_j $ for $ j = 0,1, \ ldots, N $. Another possibility is to look for a function that fits the data in order to minimize errors between $ p (x_j) $ and $ y_j $ at all points. Polynomials are very simple functions and are therefore widely used for these approximations. In this project will be seen more generally interpolation methods, spline, uniform approximation and further studied the adjustment of least squares with weighted error and their relationship with orthogonal polynomials.

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