Physical Sciences and Mathematics Commons^™

A Comprehensive Survey On Functional Approximation, Yucheng Hua

Honors Projects

The theory of functional approximation has numerous applications in sciences and industry. This thesis focuses on the possible approaches to approximate a continuous function on a compact subset of R² using a variety of constructions. The results are presented from the following four general topics: polynomials, Fourier series, wavelets, and neural networks. Approximation with polynomials on subsets of R leads to the discussion of the Stone-Weierstrass theorem. Convergence of Fourier series is characterized on the unit circle. Wavelets are introduced following the Fourier transform, and their construction as well as ability to approximate functions in L²(R) is …