I am learning some Numerical Analysis from video lectures posted on Justin Solomon's YouTube channel. I will try implementing some of the stuff I learn, and I will put it here.

• kahan - a simple algorithm for summing up numbers without error.
• linalg/ludecomp - decompose a matrix A into PAQ=LU, then use the factorized form to solve Ax=b.
• linalg/cholesky - decompose symmetric positive-definite matrices using Cholesky factorization.
• linalg/qrdecomp - decompose any matrix A into QR using various methods.
• linalg/leastsquares - use QR decomposition for more stable least-squares approximations.
• linalg/eigen - approximate the eigenpairs of some matrices.
• linalg/svd - compute Singular Value Decompositions of matrices.
• realroots - approximate the roots of arbitrary single-variable functions.
• mvroots - approximate the roots of multi-variable functions and complex polynomials.
• unitcircles - a simple HTML app to visualize different p-norms.
• regression - basic regression using least squares.
• imagealign - align a crooked image to a reference image using least squares.
• newton-basins - visualize the "Newton Basins" of polynomials.
• conjgrad - basic Conjugate Gradient implementation.
• blurify - blur or sharpen an image.
• interp - various interpolation algorithms.
• interp/visualizer - visualize interpolations.
• integration - numerical integration using polynomial approximations.
• autodiff - a basic automatic differentiation system.