approximation-theory

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

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.

Python codes, synthetic data, figures, and numerical results for symmetric neural network approximation in Banach spaces.

Preliminary numerical experiments for some greedy algorithms.

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).

Function code in python of The fourth order Runge Kutta method to compute approximated solutions of ordinary differential equations and its documentation.

Code for the technical note "Chebyshev-Controlled Chernoff Approximations of the Heat Semigroup" (doi:10.5281/zenodo.21708475).

A port of Chebfun from MATLAB to GNU Octave.

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

Challenge of shallow neural network approximation with one-dimensional input.

A collection of notes on introductory numerical analysis, involving multiple methods.

Composite Polynomial Approximations to the Sign and Sqrt Functions