00000ctm a22000004a 4500 UP-99796217612791157 Buklod 20180613093506.0 m |o d | ta 180613s2009 xx d r |||| u| (iLib)UPD-00363112327 DARCHIVES rda eng DMLUC LG 996 2009 M38 T36 Tampos, Arnel L. author. A pade-chebyshev resolution of the Gibbs phenomenon in function approximation by Arnel L. Tampos ;thesis adviser, Jose Ernie C. Lope. Quezon City Institute of Mathematics, College of Science, University of the Philippines Diliman 2009. 138 leaves illustrations 28 cm text rdacontent unmediated rdamedia volume rdacarrier Thesis (Ph.D. Mathematics)--University of the Philippines Diliman April 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. Pade approximant. Approximation theory. Polynomials. Lope, Jose Ernie C. thesis adviser. FI UPD DARCHIVES LG 996 2009 M38 T36 Thesis