Approximation Theory and Applications

Dear Colleagues,

Approximation theory is an important bridge between pure and applied mathematics since it consists of a theoretical study of methods that use numerical approximation to solve problems of mathematical analysis by means of computational algorithms and computer simulation. After more than a century from the seminal works of Bernstein and Chebyshev (among others), approximation theory is now a very extensive branch of mathematics, interlacing with many various other scientific fields. In fact, it plays a central role in the analysis of numerical methods for mathematical, physical, medical, engineering, and social sciences and provides directions for future research. For example, polynomial approximation is the basis for the study of Gaussian rules; spline and radial basis function interpolation is an important tool in the geometric design of automotive and aerospatial vessels, while wavelets and their generalizations are used for the compression of large digital images and videos. Recently, approximation methods have been applied to the construction of numerical methods for integral and partial differential equations, fractional calculus, signal theory, and deep learning.

The aim of this Special Issue of Mathematics is to collect the state-of-the-art improvements of several aspects of approximation theory and of its both theoretical and applied branches and connections with other applied and computational sciences. Thus, research papers and review articles, considering the developments of approximation theory, as well as problems in which approximation theory plays a significant role, are welcome.

Dr. Paola Lamberti
Prof. Dr. Incoronata Notarangelo
Guest Editors

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