Numerical linear algebra
by Lloyd N. Trefethen · first published 1997
90% recommend10% neutral
Why HN recommends it
Graduate-level text on how matrix algorithms work, with intuitive treatment of the SVD, eigenvalues, LU, and iterative methods. Suits readers who know basic linear algebra and want a computational view.
Summarised by Claude from recommending comments
An introduction to the field of numerical linear algebra. It aims to present the core, standard material in a novel way. Topics include iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability.
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…wouldn't quite fit (despite me finding it to be pretty cool, and these methods sort of eating the lunch of most other inverse methods). I'd round out the course maybe with a read through of Trefethen-Bau, “Numerical Linear Algebra” for those new to the topic area.
on “Computational Linear Algebra” ↗…for iterative methods are also important. Hell, even efficient direct techniques embedded in indirect solvers is important. Part of the way to get started would be to look at something like a general numerical linear algebra book like Numerical Linear Algebra from Trefethen and Bau. There are better computational algorithms than what they present, but they do a good job at introducing important factorizations and why we…
on “LU Factorization and Linear Systems for Programers” ↗Folks looking for introductory books in this area may also enjoy this new in-progress book: https://web.stanford.edu/~boyd/vmls/ As a follow-up I would recommend Trefethen & Bau, Numerical Linear Algebra.
on “Fundamentals of Linear Algebra and Optimization [pdf]” ↗Another great "intermediate" textbook (in my opinion) is Trefethen's Numerical Linear Algebra [1]. Much more readable than Golub's I would say, which is more like a reference than a textbook. [1]: https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefet...
on “Self Studying the MIT Applied Math Curriculum” ↗The two classic graduate texts for numerical linear algebra are Matrix Computations by Golub and Van Loan and Numerical Linear Algebra by Trefethen and Bau. The reference you are looking for (includes executable C++) is Numerical Recipes by William Press et al.…
on “Numerical Linear Algebra for Programmers” ↗For a great introduction to numerical linear algebra, I cannot recommend enough the book from Trefethen and Bau. Or Golub & Van Loan, if you like pain.
on “Numerical Linear Algebra for Programmers” ↗I recommend Numerical Linear Algebra by Trefethen and Bau. Thanks for this excellent link.
on “Seven sins of numerical linear algebra” ↗…fun and numerical analysis has this reputation of being dry. If you actually made them write stuff like a Navier-Stokes solver, you would get them interested. By the way if you want to learn more about numerical linear algebra, which is the cornerstone of most scientific and high performance computing, I personally enjoy Trefethen and Bau's book. Although it's aimed at a mathematical audience and assumes such.
on “Web GL Ocean Simulation” ↗The author mentions Trefethen-Bau, “Numerical Linear Algebra” as a good reference. I couldn't agree more, it's a great resource.
on “The Zen of Gradient Descent” ↗Trefethen & Bau's "Numerical Linear Algebra" is a pretty good primer, though the last few chapters I remember being a bit lacking (it's been about 6 years though).
on “The Mathematics Autodidact’s Aid (2005) [pdf]” ↗For a deeper look, Trefethen's Numerical Linear Algebra starts with these ideas and applies them to matrix algorithms.
on “Hacker's Guide to Numerical Analysis” ↗I started from zero, and my approach was to read Nocedal/Wright cover-to-cover, and then the same with "Numerical Linear Algebra" by Trefethen/Bau. Usually it goes the other way, but I found the linear algebra primer in N/W to be good enough to get started. I also read "Practical Optimization" by Murray/Gill, which is interesting…
on “Ask HN: Literature for mathematical optimization?” ↗…stability in comparison to the naive algorithm (although the page could be improved quite a bit). If your college textbooks do not mention error analysis, conditioning and stability then they are not numerical linear algebra books worthy of the name. Check out a reference like Trefethen and Bau's Numerical Linear Algebra for example. This book has a whole part (out of the 7 parts in the book) talking about conditioning and…
on “On AlphaTensor’s new matrix multiplication algorithms” ↗Numerical Linear Algebra by Trefethen and Bau.
on “Ask HN: What's the best textbook you've read?” ↗…http://www.fceia.unr.edu.ar/~fisicomp/apuntes/biblios/altnr.... In addition to those suggestions, here are a few more relevant to the present discussion. For dense matrices and how to think about linear algebra algorithms, I highly recommend Trefethen and Bau "Numerical Linear Algebra". For sparse direct solvers, Tim Davis' book (http://www.ec-securehost.com/SIAM/FA02.html) is good, and you can transition from the "learning"-level implementation to Umfpack which is his production-quality…
on “Don’t invert that matrix” ↗