{"id":1655,"date":"2023-11-13T04:32:28","date_gmt":"2023-11-13T04:32:28","guid":{"rendered":"https:\/\/www.ethanepperly.com\/?page_id=1655"},"modified":"2025-08-13T22:33:23","modified_gmt":"2025-08-13T22:33:23","slug":"posts-by-topic","status":"publish","type":"page","link":"https:\/\/www.ethanepperly.com\/index.php\/posts-by-topic\/","title":{"rendered":"Posts by Topic"},"content":{"rendered":"\n<p><strong>Big ideas in applied math<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/05\/30\/big-ideas-in-applied-math-markov-chains\/\">Markov chains<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2022\/08\/02\/big-ideas-in-applied-math-concentration-inequalities\/\">Concentration inequalities<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2021\/10\/26\/big-ideas-in-applied-math-low-rank-matrices\/\">Low-rank matrices<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2021\/05\/10\/big-ideas-in-applied-math-the-fast-fourier-transform\/\">The fast Fourier transform<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2020\/08\/09\/big-ideas-in-applied-math-galerkin-approximation\/\">Galerkin approximation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2020\/07\/18\/big-ideas-in-applied-math-sparse-matrices\/\">Sparse matrices<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2020\/07\/15\/big-ideas-in-applied-math-smoothness-and-degree-of-approximation\/\">Smoothness and degree of approximation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2020\/07\/09\/big-ideas-in-applied-math-the-schur-complement\/\">The Schur complement<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Markov musings (introduction to the mathematical analysis of Markov chains)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/06\/29\/markov-musings-1-the-fundamental-theorem\/\">The fundamental theorem<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/07\/05\/markov-musings-2-couplings\/\">Couplings<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/07\/13\/markov-musings-3-spectral-theory\/\">Spectral theory<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/08\/16\/markov-musings-4-should-you-be-lazy\/\">Should you be lazy?<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2025\/05\/22\/markov-musings-5-poincare-inequalities\/\">Poincar\u00e9 inequalities<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Low-rank approximation toolbox<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2022\/10\/11\/low-rank-approximation-toolbox-nystrom-approximation\/\">What is Nystr\u00f6m approximation?<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2022\/10\/24\/nystrom-cholesky-and-schur\/\">Nystr\u00f6m approximation, Cholesky factorization, and the Schur complement<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/06\/12\/low-rank-approximation-toolbox-randomized-svd\/\">Randomized SVD<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/06\/22\/low-rank-approximation-toolbox-analysis-of-the-randomized-svd\/\">Analysis of the randomized SVD<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/12\/07\/low-rank-approximation-toolbox-the-gram-correspondence\/\">The Gram correspondence<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Sketching<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/11\/13\/does-sketching-work\/\">Does sketching work?<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/11\/27\/which-sketch-should-i-use\/\">Which sketch should I use?<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/11\/19\/note-to-self-sketch-and-solve-with-a-gaussian-embedding\/\">Exact results for sketch-and-solve with a Gaussian embedding<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2025\/02\/12\/note-to-self-how-accurate-is-sketch-and-solve\/\">How accurate is sketch-and-solve?<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Trace estimation<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/01\/26\/stochastic-trace-estimation\/\">Stochastic trace estimation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/01\/04\/how-good-can-stochastic-trace-estimates-be\/\">How good can stochastic trace estimates be?<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/01\/28\/dont-use-gaussians-in-stochastic-trace-estimation\/\">Don&#8217;t use Gaussians in stochastic trace estimation<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Randomized Kaczmarz<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/12\/02\/randomized-kaczmarz-is-asympotically-unbiased-for-least-squares\/\">Randomized Kaczmarz is asymptotically unbiased for least squares<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2025\/06\/16\/randomized-kaczmarz-how-should-you-sample\/\">Randomized Kaczmarz: How should you sample?<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Neat randomized algorithms<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2025\/06\/07\/a-neat-not-randomized-algorithm-the-polar-express\/\">Polar express<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/07\/02\/neat-randomized-algorithms-randdiag-for-rapidly-diagonalizing-normal-matrices\/\">RandDiag for rapidly diagonalizing non-normal matrices<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/06\/25\/neat-randomized-algorithms-randomized-cholesky-qr\/\">Randomized CholeskyQR<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Numerical linear algebra: Do&#8217;s and don&#8217;ts<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2022\/07\/26\/dont-solve-the-normal-equations\/\">Don&#8217;t solve the normal equations<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2021\/03\/18\/the-better-way-to-convert-an-svd-into-a-symmetric-eigenvalue-problem\/\">The better way to convert an SVD into a symmetric eigenvalue problem<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Explainers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2025\/08\/13\/vandermonde-matrices-are-merely-exponentially-ill-conditioned\/\">Vandermonde matrices are <em>merely<\/em> exponentially ill-conditioned<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2025\/02\/25\/the-schur-product-theorem\/\">The Schur Product theorem<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/12\/10\/my-favorite-proof-of-the-cauchy-schwarz-inequality\/\">My favorite proof of the Cauchy\u2013Schwarz inequality<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/10\/08\/rejection-sampling\/\">Rejection sampling<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/12\/01\/five-interpretations-of-kernel-quadrature\/\">Five interpretations of kernel quadrature<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2022\/08\/13\/chebyshev-polynomials\/\">Chebyshev polynomials<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2022\/07\/11\/sherman-morrison-for-integral-equations\/\">Sherman\u2013Morrison for integral equations<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2022\/06\/27\/the-vandermonde-decomposition\/\">The Vandermonde decomposition<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2021\/12\/14\/the-elegant-geometry-of-the-generalized-eigenvalue-perturbation-theory\/\">The elegant geometry of generalized eigenvalue perturbation theory<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2021\/08\/11\/why-randomized-algorithms\/\">Why randomized algorithms?<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2021\/06\/22\/minimal-rank-completions\/\">Minimal rank completions<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>High-dimensional probability<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2025\/08\/04\/gaussian-integration-by-parts\/\">Gaussian integration by parts<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/06\/05\/the-hard-way-to-prove-jensens-inequality\/\">The hard way to prove Jensen&#8217;s inequality<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2023\/02\/21\/note-to-self-norm-of-a-gaussian-random-vector\/\">Norm of a Gaussian random vector<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2022\/10\/04\/note-to-self-hanson-wright-inequality\/\">The Hanson\u2013Wright inequality<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/02\/04\/note-to-self-gaussian-hypercontractivity\/\">Gaussian hypercontractivity<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2024\/11\/04\/note-to-self-hanson-wright-and-trace-estimation-with-random-vectors-on-the-sphere\/\">Hanson\u2013Wright and trace estimation with random vectors on the sphere<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Book reviews<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2020\/07\/08\/book-review-matrix-theory-by-fuzhen-zhang\/\"><em>Matrix Theory<\/em> by Fuzhen Zhang<\/a><\/li>\n<\/ul>\n\n\n\n<p><strong>Miscellaneous<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.ethanepperly.com\/index.php\/2025\/07\/08\/five-years-of-blogging\/\">Five years of blogging<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Big ideas in applied math Markov musings (introduction to the mathematical analysis of Markov chains) Low-rank approximation toolbox Sketching Trace estimation Randomized Kaczmarz Neat randomized algorithms Numerical linear algebra: Do&#8217;s and don&#8217;ts Explainers High-dimensional probability Book reviews Miscellaneous<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1655","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.ethanepperly.com\/index.php\/wp-json\/wp\/v2\/pages\/1655","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ethanepperly.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ethanepperly.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ethanepperly.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ethanepperly.com\/index.php\/wp-json\/wp\/v2\/comments?post=1655"}],"version-history":[{"count":16,"href":"https:\/\/www.ethanepperly.com\/index.php\/wp-json\/wp\/v2\/pages\/1655\/revisions"}],"predecessor-version":[{"id":2220,"href":"https:\/\/www.ethanepperly.com\/index.php\/wp-json\/wp\/v2\/pages\/1655\/revisions\/2220"}],"wp:attachment":[{"href":"https:\/\/www.ethanepperly.com\/index.php\/wp-json\/wp\/v2\/media?parent=1655"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}