approximation-theory

first commit

Code for the paper "Rational neural networks", NeurIPS 2020

Numerical study of sine approximation in MATLAB using Taylor recurrences, range reduction, Chebyshev polynomials, Clenshaw evaluation, floating-point analysis, benchmarking, tests, and reproducible CI.

Codes for the paper 'Rational Neural Networks for Approximating Jump Discontinuities of Graph Convolution Operator' ICDM 18

This directory contains lecture notes for an undergraduate numerical analysis course offered in Spring 2018, at UT Austin.

Neural network architecture with learnable fractional power bases

Official code repo for STAI-X 2026 paper "Transformer as Provable Approximators of Sparse Principal Component Analysis".

From the Weierstrass M-test to the RBF kernel: uniform convergence with explicit error bounds, applied to kernel methods and Gaussian blur

Numerical study of convergence rates for approximating transport maps

A numerical methods project exploring different approaches to computing trigonometric functions. Combining modern C++, Python, and LaTeX to investigate approximation algorithms through reproducible numerical experiments.

Description: A straightedge-and-compass constructible cubic error cascade for approximate angle trisection.

Preliminary numerical experiments for some greedy algorithms.

Volume VII of Learning Real Analysis: Numerical analysis and approximation theory.

Reproducible code, data and figures for the paper "Optimal selection of the preserved exponential in Szász–Mirakyan operators: a leading-term criterion validated at finite n" (submitted to DRNA).

Preprint and reproducibility materials for sharp closure thresholds for two-hidden-layer ReLU networks.

Numerical methods in Python: polynomial interpolation, RBF interpolation, error analysis and optimization. ``

Proof 7: Why the Cantor function (Devil's Staircase) is structurally hard for ReLU networks. All theorems verified.

Bernstein's constant to ten rigorously certified digits: beta = 0.2801694990, proved in interval arithmetic (Arb) where the 1985 Varga-Carpenter rigorous enclosure gives five. OEIS A073001. Every number re-derivable from the shipped data in exact arithmetic.

A port of Chebfun from MATLAB to GNU Octave.