Newton-Gregory Interpolation
Interpolate equally-spaced data efficiently and discover its connection to Taylor series.
Algorithms
BKM
Compute logarithms and exponentials without a floating point unit.
CORDIC
Compute sine, cosine, and exponentials using only addition, subtraction, and bit shifts.
The AAA Algorithm
Fit rational functions to data with poles and discontinuities where polynomials fail.
Tanhsinh Quadrature
Tackle tricky integrals with endpoint singularities using a clever variable transformation.
Lagrange Interpolation
Approximate functions using polynomial interpolation without solving linear systems.
Optimization
Golden Section Search for Robust Regression
Golden section search reuses objective evaluations to efficiently minimize 1D functions. Learn how this classical algorithm connects to the golden ratio and ...
Lagrange Duality
Derive and interpret the dual form of an optimization problem.
Quadratic Penalty Algo
Solve constrained optimization problems using your favorite unconstrained solver.
Nonlinear Least Squares
Fit nonlinear models using Gauss-Newton and Levenberg-Marquardt algorithms.
Visualization
Plotting Ellipses
Plot ellipses using conic, quadratic, and parametric representations.
3D Plotting using Non-Rectangular Grids
Create cleaner 3D surface plots using radial and elliptical grids in matplotlib.
Machine Learning
Numpy Regression Trees
Implement a regression tree from scratch using only numpy.
Statistics
Chatterjee’s Xi Coefficient
Detect nonlinear relationships that Pearson and Spearman miss.