41554 blogs · [ { "id": "01a08775-628c-73ca-98fb-066abc501ace", "title": "Low-Rank Approximation Toolbox: Generalized Nyström Approximation", "url": "https://www.ethanepperly.com/index.php/2026/05/20/low-rank-approximation-toolbox-generalized-nystrom-approximation/", "published_at": "2026-05-20T13:19:40+00:00" }, { "id": "01a08775-628c-73ca-98fb-066abd11aabb", "title": "Note to Self: Trace Estimation with Tensor Products", "url": "https://www.ethanepperly.com/index.php/2026/03/03/note-to-self-trace-estimation-with-tensor-products/", "published_at": "2026-03-03T02:58:28+00:00" }, { "id": "01a08775-628c-73ca-98fb-066abd9a919f", "title": "The Other Markov’s Inequality", "url": "https://www.ethanepperly.com/index.php/2026/01/16/the-other-markovs-inequality/", "published_at": "2026-01-16T20:41:15+00:00" }, { "id": "01a08775-628c-73ca-98fb-066abe14a722", "title": "Vandermonde Matrices are Merely Exponentially Ill-Conditioned", "url": "https://www.ethanepperly.com/index.php/2025/08/13/vandermonde-matrices-are-merely-exponentially-ill-conditioned/", "published_at": "2025-08-13T22:07:54+00:00" }, { "id": "01a08775-628c-73ca-98fb-066abe9ce6d7", "title": "Gaussian Integration by Parts", "url": "https://www.ethanepperly.com/index.php/2025/08/04/gaussian-integration-by-parts/", "published_at": "2025-08-04T23:57:01+00:00" }, { "id": "01a08775-628c-73ca-98fb-066abf1e8cce", "title": "Five Years of Blogging", "url": "https://www.ethanepperly.com/index.php/2025/07/08/five-years-of-blogging/", "published_at": "2025-07-08T21:33:06+00:00" }, { "id": "01a08775-628c-73ca-98fb-066abf783775", "title": "Randomized Kaczmarz: How Should You Sample?", "url": "https://www.ethanepperly.com/index.php/2025/06/16/randomized-kaczmarz-how-should-you-sample/", "published_at": "2025-06-16T14:04:00+00:00" }, { "id": "01a08775-628c-73ca-98fb-066abfc6a661", "title": "A Neat Not-Randomized Algorithm: Polar Express", "url": "https://www.ethanepperly.com/index.php/2025/06/07/a-neat-not-randomized-algorithm-the-polar-express/", "published_at": "2025-06-07T01:56:10+00:00" }, { "id": "01a08775-628c-73ca-98fb-066ac06ae108", "title": "Markov Musings 5: Poincaré Inequalities", "url": "https://www.ethanepperly.com/index.php/2025/05/22/markov-musings-5-poincare-inequalities/", "published_at": "2025-05-22T18:53:57+00:00" }, { "id": "01a08775-628c-73ca-98fb-066ac14caee7", "title": "The Schur Product Theorem", "url": "https://www.ethanepperly.com/index.php/2025/02/25/the-schur-product-theorem/", "published_at": "2025-02-25T03:18:39+00:00" }, { "id": "01a0c50b-c4d8-724d-a162-54ea0570a34d", "title": "Note to Self: How Accurate is Sketch and Solve?", "url": "https://www.ethanepperly.com/index.php/2025/02/12/note-to-self-how-accurate-is-sketch-and-solve/", "published_at": "2025-02-12T02:09:19+00:00" }, { "id": "01a0c50b-c4d8-724d-a162-54ea05efdb3b", "title": "My Favorite Proof of the Cauchy–Schwarz Inequality", "url": "https://www.ethanepperly.com/index.php/2024/12/10/my-favorite-proof-of-the-cauchy-schwarz-inequality/", "published_at": "2024-12-10T21:40:07+00:00" }, { "id": "01a0c50b-c4d8-724d-a162-54ea069e479d", "title": "Low-Rank Approximation Toolbox: The Gram Correspondence", "url": "https://www.ethanepperly.com/index.php/2024/12/07/low-rank-approximation-toolbox-the-gram-correspondence/", "published_at": "2024-12-07T00:50:26+00:00" }, { "id": "01a0c50b-c4d8-724d-a162-54ea06ea57cf", "title": "Randomized Kaczmarz is Asympotically Unbiased for Least Squares", "url": "https://www.ethanepperly.com/index.php/2024/12/02/randomized-kaczmarz-is-asympotically-unbiased-for-least-squares/", "published_at": "2024-12-02T18:21:11+00:00" }, { "id": "01a0c50b-c4d8-724d-a162-54ea077679ff", "title": "Note to Self: Sketch-and-Solve with a Gaussian Embedding", "url": "https://www.ethanepperly.com/index.php/2024/11/19/note-to-self-sketch-and-solve-with-a-gaussian-embedding/", "published_at": "2024-11-19T22:13:03+00:00" }, { "id": "01a0c50b-c4d8-724d-a162-54ea080e13b3", "title": "Note to Self: Hanson–Wright and Trace Estimation with Random Vectors on the Sphere", "url": "https://www.ethanepperly.com/index.php/2024/11/04/note-to-self-hanson-wright-and-trace-estimation-with-random-vectors-on-the-sphere/", "published_at": "2024-11-04T03:56:55+00:00" }, { "id": "01a0c50b-c4d8-724d-a162-54ea0815883f", "title": "Rejection Sampling", "url": "https://www.ethanepperly.com/index.php/2024/10/08/rejection-sampling/", "published_at": "2024-10-08T17:09:41+00:00" }, { "id": "01a0c50b-c4d8-724d-a162-54ea088fe77b", "title": "Neat Randomized Algorithms: RandDiag for Rapidly Diagonalizing Normal Matrices", "url": "https://www.ethanepperly.com/index.php/2024/07/02/neat-randomized-algorithms-randdiag-for-rapidly-diagonalizing-normal-matrices/", "published_at": "2024-07-02T16:04:48+00:00" }, { "id": "01a0c50b-c4d8-724d-a162-54ea09062f77", "title": "Neat Randomized Algorithms: Randomized Cholesky QR", "url": "https://www.ethanepperly.com/index.php/2024/06/25/neat-randomized-algorithms-randomized-cholesky-qr/", "published_at": "2024-06-25T19:28:53+00:00" }, { "id": "01a0c50b-c4d8-724d-a162-54ea099f94fd", "title": "Note to Self: Gaussian Hypercontractivity", "url": "https://www.ethanepperly.com/index.php/2024/02/04/note-to-self-gaussian-hypercontractivity/", "published_at": "2024-02-04T22:29:09+00:00" }, { "id": "01a0c51b-53df-70ac-bc85-71e1e68ae014", "title": "Don’t Use Gaussians in Stochastic Trace Estimation", "url": "https://www.ethanepperly.com/index.php/2024/01/28/dont-use-gaussians-in-stochastic-trace-estimation/", "published_at": "2024-01-28T02:53:09+00:00" }, { "id": "01a0c51b-53e0-7162-bfc8-96dde59583e1", "title": "How Good Can Stochastic Trace Estimates Be?", "url": "https://www.ethanepperly.com/index.php/2024/01/04/how-good-can-stochastic-trace-estimates-be/", "published_at": "2024-01-04T01:16:58+00:00" }, { "id": "01a0c51b-53e0-7162-bfc8-96dde5fff495", "title": "Five Interpretations of Kernel Quadrature", "url": "https://www.ethanepperly.com/index.php/2023/12/01/five-interpretations-of-kernel-quadrature/", "published_at": "2023-12-01T17:25:39+00:00" }, { "id": "01a0c51b-53e0-7162-bfc8-96dde64b7f25", "title": "Which Sketch Should I Use?", "url": "https://www.ethanepperly.com/index.php/2023/11/27/which-sketch-should-i-use/", "published_at": "2023-11-27T17:09:04+00:00" }, { "id": "01a0c51b-53e0-7162-bfc8-96dde69aa197", "title": "Does Sketching Work?", "url": "https://www.ethanepperly.com/index.php/2023/11/13/does-sketching-work/", "published_at": "2023-11-13T19:19:18+00:00" }, { "id": "01a0c51b-53e0-7162-bfc8-96dde7462a7c", "title": "Markov Musings 4: Should You Be Lazy?", "url": "https://www.ethanepperly.com/index.php/2023/08/16/markov-musings-4-should-you-be-lazy/", "published_at": "2023-08-16T03:49:04+00:00" }, { "id": "01a0c51b-53e0-7162-bfc8-96dde7744364", "title": "Markov Musings 3: Spectral Theory", "url": "https://www.ethanepperly.com/index.php/2023/07/13/markov-musings-3-spectral-theory/", "published_at": "2023-07-13T15:48:59+00:00" }, { "id": "01a0c51b-53e0-7162-bfc8-96dde8321760", "title": "Markov Musings 2: Couplings", "url": "https://www.ethanepperly.com/index.php/2023/07/05/markov-musings-2-couplings/", "published_at": "2023-07-05T18:45:31+00:00" }, { "id": "01a0c51b-53e0-7162-bfc8-96dde908abeb", "title": "Markov Musings 1: The Fundamental Theorem", "url": "https://www.ethanepperly.com/index.php/2023/06/29/markov-musings-1-the-fundamental-theorem/", "published_at": "2023-06-29T18:29:59+00:00" }, { "id": "01a0c51b-53e0-7162-bfc8-96dde9c7bec1", "title": "Low-Rank Approximation Toolbox: Analysis of the Randomized SVD", "url": "https://www.ethanepperly.com/index.php/2023/06/22/low-rank-approximation-toolbox-analysis-of-the-randomized-svd/", "published_at": "2023-06-22T00:51:51+00:00" }, { "id": "01a0c526-83c9-735a-91bf-3662ada10bfd", "title": "Low-Rank Approximation Toolbox: Randomized SVD", "url": "https://www.ethanepperly.com/index.php/2023/06/12/low-rank-approximation-toolbox-randomized-svd/", "published_at": "2023-06-12T14:25:57+00:00" }, { "id": "01a0c526-83c9-735a-91bf-3662ae93d5b6", "title": "The Hard Way to Prove Jensen’s Inequality", "url": "https://www.ethanepperly.com/index.php/2023/06/05/the-hard-way-to-prove-jensens-inequality/", "published_at": "2023-06-05T21:45:55+00:00" }, { "id": "01a0c526-83c9-735a-91bf-3662af6c36ac", "title": "Big Ideas in Applied Math: Markov Chains", "url": "https://www.ethanepperly.com/index.php/2023/05/30/big-ideas-in-applied-math-markov-chains/", "published_at": "2023-05-30T17:29:10+00:00" }, { "id": "01a0c526-83c9-735a-91bf-3662b04a5e71", "title": "Note to Self: Norm of a Gaussian Random Vector", "url": "https://www.ethanepperly.com/index.php/2023/02/21/note-to-self-norm-of-a-gaussian-random-vector/", "published_at": "2023-02-21T17:28:11+00:00" }, { "id": "01a0c526-83c9-735a-91bf-3662b10a901d", "title": "Stochastic Trace Estimation", "url": "https://www.ethanepperly.com/index.php/2023/01/26/stochastic-trace-estimation/", "published_at": "2023-01-26T19:29:34+00:00" }, { "id": "01a0c526-83c9-735a-91bf-3662b16f1cd2", "title": "Low-Rank Approximation Toolbox: Nyström, Cholesky, and Schur", "url": "https://www.ethanepperly.com/index.php/2022/10/24/nystrom-cholesky-and-schur/", "published_at": "2022-10-24T15:08:46+00:00" }, { "id": "01a0c526-83c9-735a-91bf-3662b1e68a18", "title": "Low-Rank Approximation Toolbox: Nyström Approximation", "url": "https://www.ethanepperly.com/index.php/2022/10/11/low-rank-approximation-toolbox-nystrom-approximation/", "published_at": "2022-10-11T15:30:07+00:00" }, { "id": "01a0c526-83c9-735a-91bf-3662b2e27d18", "title": "Note to Self: Hanson–Wright Inequality", "url": "https://www.ethanepperly.com/index.php/2022/10/04/note-to-self-hanson-wright-inequality/", "published_at": "2022-10-04T15:54:58+00:00" }, { "id": "01a0c526-83c9-735a-91bf-3662b3299677", "title": "Chebyshev Polynomials", "url": "https://www.ethanepperly.com/index.php/2022/08/13/chebyshev-polynomials/", "published_at": "2022-08-13T22:59:51+00:00" }, { "id": "01a0c526-83c9-735a-91bf-3662b4210730", "title": "Big Ideas in Applied Math: Concentration Inequalities", "url": "https://www.ethanepperly.com/index.php/2022/08/02/big-ideas-in-applied-math-concentration-inequalities/", "published_at": "2022-08-02T14:55:51+00:00" } ] posts Claim your blog

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2026

Low-Rank Approximation Toolbox: Generalized Nyström Approximation original ↗

20 May 2026

Note to Self: Trace Estimation with Tensor Products original ↗

3 Mar 2026

The Other Markov’s Inequality original ↗

16 Jan 2026

2025

Vandermonde Matrices are Merely Exponentially Ill-Conditioned original ↗

13 Aug 2025

Gaussian Integration by Parts original ↗

4 Aug 2025

Five Years of Blogging original ↗

8 Jul 2025

Randomized Kaczmarz: How Should You Sample?original ↗

16 Jun 2025

A Neat Not-Randomized Algorithm: Polar Express original ↗

7 Jun 2025

Markov Musings 5: Poincaré Inequalities original ↗

22 May 2025

The Schur Product Theorem original ↗

25 Feb 2025

Note to Self: How Accurate is Sketch and Solve?original ↗

12 Feb 2025

2024

My Favorite Proof of the Cauchy–Schwarz Inequality original ↗

10 Dec 2024

Low-Rank Approximation Toolbox: The Gram Correspondence original ↗

7 Dec 2024

Randomized Kaczmarz is Asympotically Unbiased for Least Squares original ↗

2 Dec 2024

Note to Self: Sketch-and-Solve with a Gaussian Embedding original ↗

19 Nov 2024

Note to Self: Hanson–Wright and Trace Estimation with Random Vectors on the Sphere original ↗

4 Nov 2024

Rejection Sampling original ↗

8 Oct 2024

Neat Randomized Algorithms: RandDiag for Rapidly Diagonalizing Normal Matrices original ↗

2 Jul 2024

Neat Randomized Algorithms: Randomized Cholesky QR original ↗

25 Jun 2024

Note to Self: Gaussian Hypercontractivity original ↗

4 Feb 2024

Don’t Use Gaussians in Stochastic Trace Estimation original ↗

28 Jan 2024

How Good Can Stochastic Trace Estimates Be?original ↗

4 Jan 2024

2023

Five Interpretations of Kernel Quadrature original ↗

1 Dec 2023

Which Sketch Should I Use?original ↗

27 Nov 2023

Does Sketching Work?original ↗

13 Nov 2023

Markov Musings 4: Should You Be Lazy?original ↗

16 Aug 2023

Markov Musings 3: Spectral Theory original ↗

13 Jul 2023

Markov Musings 2: Couplings original ↗

5 Jul 2023

Markov Musings 1: The Fundamental Theorem original ↗

29 Jun 2023

Low-Rank Approximation Toolbox: Analysis of the Randomized SVD original ↗

22 Jun 2023

Low-Rank Approximation Toolbox: Randomized SVD original ↗

12 Jun 2023

The Hard Way to Prove Jensen’s Inequality original ↗

5 Jun 2023

Big Ideas in Applied Math: Markov Chains original ↗

30 May 2023

Note to Self: Norm of a Gaussian Random Vector original ↗

21 Feb 2023

Stochastic Trace Estimation original ↗

26 Jan 2023

2022

Low-Rank Approximation Toolbox: Nyström, Cholesky, and Schur original ↗

24 Oct 2022

Low-Rank Approximation Toolbox: Nyström Approximation original ↗

11 Oct 2022

Note to Self: Hanson–Wright Inequality original ↗

4 Oct 2022

Chebyshev Polynomials original ↗

13 Aug 2022

Big Ideas in Applied Math: Concentration Inequalities original ↗

2 Aug 2022