A pade-chebyshev resolution of the Gibbs phenomenon in function approximation - Tampos, Arnel L.; Lope, Jose Ernie C. (Quezon City Institute of Mathematics, College of Science, University of the Philippines Diliman, 2009)
The occurence of the Gibbs phenomenon is an undesirable peculiarity in approximating functions with finite jumps by partial sums of an orthogonal series expansion, causing non-uniform convergence near the points of discontinuities and slow convergence elsewhere in the domain under consideration. Rational approximation, notably Pade-type approximation, is a way of reducing the adverse effect of such phenomenon for a better reconstruction of the function. Using the trigonometric definition of the Chebyshev polynomials which allows a transformation leading to the Laurent series expansion of the function, we aim to resolve the Gibbs phenomenon by constructing an amplified PadeChebysshev approximant based on the concept introduced by Driscoll and Fornberg in [12,13] which incorporates into the approximation process the singularities of the function.
Thesis (Ph.D. Mathematics)--University of the Philippines Diliman
Keywords: Pade approximant; Approximation theory; Polynomials