Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1992. / Includes bibliographical references (p. 85-89).

Thesis (Ph. D.)--University of Delaware, 2005. / Principal faculty advisor: Tobin A. Driscoll, Dept. of Mathematical Sciences. Includes bibliographical references.

Thesis (Ph. D. in Mathematics)--Vanderbilt University, Aug. 2006. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (leaves 65-72).

D.Phil. (Applied mathematics) / Please refer to full text to view abstract

Orientador: Sérgio Antonio Tozoni / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-22T06:19:51Z (GMT). No. of bitstreams: 1 Lopes_RaquelVieira_M.pdf: 1141005 bytes, checksum: 8091e673668abab031630ae7fd1b7436 (MD5) Previous issue date: 2013 / Resumo: Os sk-splines são uma generalização natural dos splines polinomiais, os quais foram introduzidos e tiveram sua teoria básica desenvolvida por Alexander Kushpel nos anos de 1983-1985. Estas funções são importantes em várias aplicações e seu espaço é gerado por translações discretas de uma única função núcleo. Neste trabalho, estudamos condições necessárias e suficientes para a existência e unicidade de sk-splines interpolantes de funções periódicas. Além disso, estudamos a aproximação de funções de determinadas classes por sk-splines nos espaços Lp. Como aplicação estudamos a aproximação de funções infinitamente diferenciáveis e finitamente diferenciáveis por sk- splines / Abstract: The sk-splines are a natural generalization of polynomial splines. They were introduced and their basic theory developed by Alexander Kushpel between 1983 and 1985. These functions are important in many applications and the space of sk-splines is the linear span of shifts of a single kernel K. In this work, we study necessary and sufficient conditions for the existence and uniqueness of sk-splines interpolants of periodic functions. Furthermore, we study the approximation in several classes of functions by sk-splines in the Lp spaces. As an application we study the approximation of infinitely and finitely differentiable functions by sk-splines / Mestrado / Matematica Aplicada / Mestra em Matemática Aplicada

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Control systems governed by nonlinear neutral functional differential equations are formulated as abstract evolution equations in product spaces. At this point existence and uniqueness of solutions are studied. This formulation is used to develop a general approximation scheme for those systems. Convergence of this scheme is analyzed. It is also shown how spline based approximating methods fall within this general framework. An illustrative example is presented. / Ph. D.

We give a method, by solving a nonlinear system of equations, for Gauss harmonic interpolation formulas which are useful for approximating, the solution of the Dirichlet problem. We also discuss approximations for integrals of the form I(f) = (1/2πi) ∫_L (f(z)/(z-α)) dz. Our approximations shall be of the form Q(f) = Σ_k=1ⁿ A_kf(τ_k). We characterize the nodes τ₁, τ₂, …, τ_n, to get the maximum precision for our formulas. Finally, we propose a general problem of approximating for linear functionals; our results need further development. / Ph. D.