The Curious Engineer

All blogs / Math

Ethan N. W. Epperly

ethanepperly.com

Computational Methods for Science, Machine Learning, and Quantum Information

MathAlgorithms / data structuresScience

’20’21’22’23’24’25’26
Posts
54 from 8 Jul 2020 to 20 May 2026
Posting
now and then (3 in the last year)
Kind
personal blog
Feed
https://www.ethanepperly.com/index.php/feed/

2026 3

  1. Low-Rank Approximation Toolbox: Generalized Nyström Approximation
  2. Note to Self: Trace Estimation with Tensor Products
  3. The Other Markov’s Inequality

2025 8

  1. Vandermonde Matrices are Merely Exponentially Ill-Conditioned
  2. Gaussian Integration by Parts
  3. Five Years of Blogging
  4. Randomized Kaczmarz: How Should You Sample?
  5. A Neat Not-Randomized Algorithm: Polar Express
  6. Markov Musings 5: Poincaré Inequalities
  7. The Schur Product Theorem
  8. Note to Self: How Accurate is Sketch and Solve?

2024 11

  1. My Favorite Proof of the Cauchy–Schwarz Inequality
  2. Low-Rank Approximation Toolbox: The Gram Correspondence
  3. Randomized Kaczmarz is Asympotically Unbiased for Least Squares
  4. Note to Self: Sketch-and-Solve with a Gaussian Embedding
  5. Note to Self: Hanson–Wright and Trace Estimation with Random Vectors on the Sphere
  6. Rejection Sampling
  7. Neat Randomized Algorithms: RandDiag for Rapidly Diagonalizing Normal Matrices
  8. Neat Randomized Algorithms: Randomized Cholesky QR
  9. Note to Self: Gaussian Hypercontractivity
  10. Don’t Use Gaussians in Stochastic Trace Estimation
  11. How Good Can Stochastic Trace Estimates Be?

2023 13

  1. Five Interpretations of Kernel Quadrature
  2. Which Sketch Should I Use?
  3. Does Sketching Work?
  4. Markov Musings 4: Should You Be Lazy?
  5. Markov Musings 3: Spectral Theory
  6. Markov Musings 2: Couplings
  7. Markov Musings 1: The Fundamental Theorem
  8. Low-Rank Approximation Toolbox: Analysis of the Randomized SVD
  9. Low-Rank Approximation Toolbox: Randomized SVD
  10. The Hard Way to Prove Jensen’s Inequality
  11. Big Ideas in Applied Math: Markov Chains
  12. Note to Self: Norm of a Gaussian Random Vector
  13. Stochastic Trace Estimation

2022 8

  1. Low-Rank Approximation Toolbox: Nyström, Cholesky, and Schur
  2. Low-Rank Approximation Toolbox: Nyström Approximation
  3. Note to Self: Hanson–Wright Inequality
  4. Chebyshev Polynomials
  5. Big Ideas in Applied Math: Concentration Inequalities
  6. Don’t Solve the Normal Equations
  7. Sherman–Morrison for Integral Equations
  8. The Vandermonde Decomposition

2021 6

  1. The Elegant Geometry of Generalized Eigenvalue Perturbation Theory
  2. Big Ideas in Applied Math: Low-rank Matrices
  3. Why Randomized Algorithms?
  4. Minimal Rank Completions
  5. Big Ideas in Applied Math: The Fast Fourier Transform
  6. The Better Way to Convert an SVD into a Symmetric Eigenvalue Problem

2020 5

  1. Big Ideas in Applied Math: Galerkin Approximation
  2. Big Ideas in Applied Math: Sparse Matrices
  3. Big Ideas in Applied Math: Smoothness and Degree of Approximation
  4. Big Ideas in Applied Math: The Schur Complement
  5. Book Review: Matrix Theory by Fuzhen Zhang