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)
Low-rank approximation toolbox
- What is Nyström approximation?
- Nyström approximation, Cholesky factorization, and the Schur complement
- Randomized SVD
- Analysis of the randomized SVD
Sketching
Trace estimation
- Stochastic trace estimation
- How good can stochastic trace estimates be?
- Don’t use Gaussians in stochastic trace estimation
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
- Five interpretations of kernel quadrature
- 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
- Gaussian hypercontractivity
Book reviews