Fourier Analysis of 2-Point Hermite Interpolatory Subdivision Schemes.
Fractal trigonometric approximation.
Fractal-classic interpolants
The methodology of fractal interpolation is very useful for processing experimental signals in order to extract their characteristics of complexity. We go further and prove that the Iterated Function System involved may also be used to obtain new approximants that are close to classical ones. In this work a classical function and a fractal function are combined to construct a new interpolant. The fractal function is first defined as a perturbation of a classical mapping. The additional condition...
Free vibration of layered circular cylindrical shells of variable thickness using spline function approximation.
Functional equations stemming from numerical analysis [Book]
Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality
We prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized Koksma-Hlawka inequality for non-uniform measures. Applications of this inequality to importance sampling in Quasi-Monte Carlo integration and tractability theory are given. We also discuss the problem of transforming a low-discrepancy sequence with respect to the uniform measure...
Fundamental quadratic splines and applications
Further convergence results for two quadrature rules for Cauchy type principal value integrals
New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Hölder condition with exponent less or equal to . The results obtained here supplement...