Posts by Topic

Big ideas in applied math

• Markov chains
• Concentration inequalities
• Low-rank matrices
• The fast Fourier transform
• Galerkin approximation
• Sparse matrices
• Smoothness and degree of approximation
• The Schur complement

Markov musings (introduction to the mathematical analysis of Markov chains)

• The fundamental theorem
• Couplings
• Spectral theory
• Should you be lazy?

Low-rank approximation toolbox

• What is Nyström approximation?
• Nyström approximation, Cholesky factorization, and the Schur complement
• Randomized SVD
• Analysis of the randomized SVD

Sketching

• Does sketching work?
• Which sketch should I use?

Numerical linear algebra: Do’s and don’ts

• Don’t solve the normal equations
• The better way to convert an SVD into a symmetric eigenvalue problem

Explainers

• Stochastic trace estimation
• Chebyshev polynomials
• Sherman–Morrison for integral equations
• The Vandermonde decomposition
• The elegant geometry of generalized eigenvalue perturbation theory
• Why randomized algorithms?
• Minimal rank completions

High-dimensional probability

• The hard way to prove Jensen’s inequality
• Norm of a Gaussian random vector
• The Hanson–Wright inequality

Book reviews

• Matrix Theory by Fuzhen Zhang