Newton-Gregory Interpolation
Interpolate equally-spaced data efficiently and discover its connection to Taylor series.
Mathematics
Lagrange Duality
Derive and interpret the dual form of an optimization problem.
Plotting Ellipses
Plot ellipses using conic, quadratic, and parametric representations.
Numpy Regression Trees
Implement a regression tree from scratch using only numpy.
Quadratic Penalty Algo
Solve constrained optimization problems using your favorite unconstrained solver.
3D Plotting using Non-Rectangular Grids
Create cleaner 3D surface plots using radial and elliptical grids in matplotlib.
Nonlinear Least Squares
Fit nonlinear models using Gauss-Newton and Levenberg-Marquardt algorithms.
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.
Lagrange Interpolation
Approximate functions using polynomial interpolation without solving linear systems.
Calculus
Tanhsinh Quadrature
Tackle tricky integrals with endpoint singularities using a clever variable transformation.
Statistics
Chatterjee’s Xi Coefficient
Detect nonlinear relationships that Pearson and Spearman miss.