报告地点：行健楼学术活动室665
邀请人：张志跃教授
Abstract: This work introduces innovative spline quasi-interpolants designed for precise data approximation in both one and multiple dimensions. The new approach aims to achieve high accuracy near function singularities, using either precise knowledge of singularity positions or automatically detecting the presence of discontinuities. This enables accurate approximation of function values close to these points. The proposed modifications include the use of nonlinear means, ideas similar to the Weighted Essentially Non-Oscillatory (WENO) algorithm, and the introduction of correction terms for B-spline quasi-interpolants. These enhancements further improve the approximation quality near singularities by effectively handling discontinuities and preserving the accuracy of the spline in smooth areas. The numerical experiments presented validate the theoretical findings, demonstrating the effectiveness of the proposed methods.
Short bio: Dr. Juan Ruiz holds a position as Professor at the Department of Applied Mathematics and Statistics, at University of Cartagena, Spain. He has participated in more than 30 international congresses and published more than 50 research articles in international journals indexed in the Journal of Scientific Reports. His research interests include nonlinear interpolation, subdivision and multiresolution methods, wavelets, nonlinear approximation, image processing and numerical methods for PDEs.
