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Calculations of the roots of classical orthogonal polynomials: an application to gaussian quadrature
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Date
2019
Author
Shaidolda, Gulnaz
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This thesis focuses on classical orthogonal polynomials namely Jacobi, Laguerre and Hermite polynomials and a method to calculate the roots of these polynomials is constructed. The roots are expressed as the eigenvalues of a tridiagonal matrix whose coefficients depend on the recurrence formula for the classical orthogonal polynomials. These approximations of roots are used as method of computation of Gaussian quadratures. Then the discussion of the numerical results are then introduced to deduce the efficiency of the method.
Subject Keywords
Gaussian quadrature formulas.
,
Functions, Orthogonal.
,
Legendre's polynomials.
,
Laguerre polynomials.
URI
http://etd.lib.metu.edu.tr/upload/12622945/index.pdf
https://hdl.handle.net/11511/27991
Collections
Graduate School of Natural and Applied Sciences, Thesis
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G. Shaidolda, “Calculations of the roots of classical orthogonal polynomials: an application to gaussian quadrature,” M.S. - Master of Science, Middle East Technical University, 2019.