Matrix computations
by Gene H. Golub · first published 1983
79% recommend21% neutral
Why HN recommends it
Standard graduate reference on numerical linear algebra, focused on how matrix algorithms are actually computed rather than ready-made code. Suits readers wanting practical depth after Strang or Trefethen and Bau.
Summarised by Claude from recommending comments
"Thoroughly revised, updated, and expanded by more than one third, this new edition of Golub and Van Loan's landmark book in scientific computing provides the vital mathematical background and algorithmic skills required for the production of numerical software. New chapters on high performance computing use matrix multiplication to show how to organize a calculation for vector processors as well as for computers with shared or distributed memories. A.so new are discussions of parallel vector methods for linear equations, least squares, and eigenvalue problems."--Back cover.
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…tell yourself that you "know" linear algebra when it would be closer to the truth to say that you used to know linear algebra, but can't answer even basic questions today. After Strang, Golub's book on Matrix Computations is also really incredible.[3] [0]: https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715C... [1]: https://www.youtube.com/watch?v=Cll03FUxjuk [2]: https://ocw.mit.edu/courses/mathematics/18-650-statistics-fo...…
on “Self Studying the MIT Applied Math Curriculum” ↗…Cambridge. Getting a full understanding of algorithmic linear algebra is also important. At some point you should feel familiar with most of the material in 10.) Golub, G., and Van Loan, C. (1996). "Matrix Computations" Johns Hopkins. It's good to know some information theory. The classic is: 11.) Cover, T. and Thomas, J. "Elements of Information Theory" Wiley. Finally, if you want to start to learn some…
on “Learning About Statistical Learning” ↗Golub's "Matrix Computations" remains a must-read reference text here: http://web.mit.edu/ehliu/Public/sclark/Golub%20G.H.,%20Van%2...
on “LU Factorization and Linear Systems for Programers” ↗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. There are a couple other…
on “Numerical Linear Algebra for Programmers” ↗…horse where it belongs. Learning to do row reduction by hand is a really pointless exercise that misses the forest for the trees. But if want want the nitty gritty on computation, Golub and Van Loans "Matrix Computations" is pretty classic.
on “Calculus Made Easy (1910)” ↗…phenomenon we see in real life follow a power law and what that means 3. Leonardo da Vinci (Walter Isaacson) - surprising how little of da Vinci's real personality is reflected in his modern image 4. Matrix computations – third edition (Gene Golub, Charles van Loan) - good read if you're into linear algebra 5. Giving effective feedback (Harvard business review) - useful for getting an understanding on how to handle…
on “Ask HN: Books you read in 2018?” ↗…may be considered well-described when there is no longer any need for a separate course to teach the notation and tricks behind it. When I was in grad school, one of my favorite books was Gene Golub’s “Matrix Computations”. It really is an impressive book from an incredible mind, like a book on chess positions written by Bobby Fisher. Regardless, it was hard for me to go through it without wondering why such a thing exists.…
on “The Philosophy of Linear Algebra (2021)” ↗…and Lemarechal, Fundamentals of convex analysis. This book has been highly recommended to me but I've never used it. Might be an easier go than Schneider for convex geometry. - Golub and van Loan, Matrix computations. Excellent book on numerical linear algebra. - Bonnans, Gilbert, Lemarechal, Sagastizabal, Numerical optimization: theoretical and practical aspects. This book has a detailed description of bundle…
on “Ask HN: Literature for mathematical optimization?” ↗…mathematical sciences contexts. There I would suggest, e.g., Boyd and Vandenberghe’s Introduction to Applied Linear Algebra [1], Meyer’s Matrix Analysis and Applied Linear Algebra [2], Golub and Van Loan’s Matrix Computations [3] etc. > But the book doesn’t like determinants and isn’t focused on computing things around matrices [...]. This is purposeful. [1] https://web.stanford.edu/~boyd/vmls [2] http://matrixanalysis.com…
on “You're not dumb, the prerequisites are bullshit” ↗If you're looking for a better book, I can recommend: Matrix computations, by Golub and van Loan.
on “Boycott Numerical Recipes (2007)” ↗Linear Algebra by Axler Matrix Computations by Golub Collaborative filtering papers by Koren: http://research.yahoo.com/Yehuda_Koren Stanford paper which is the source of Mahout project: http://www.cs.stanford.edu/people/ang//papers/nips06-mapredu...…
on “Numerical recipes in Hadoop” ↗I don't know how Matrix computations wasn't mentioned. When it comes to practical implementations of linear algebra concepts this book is your best friend. [1] http://www.amazon.com/Computations-Hopkins-Studies-Mathemati...
on “No-bullshit guide to linear algebra” ↗It's been a few years since I did serious computational linear algebra, but at that time Matrix Computations by Golub and van Loan seemed to be the standard textbook in the circles I moved in. Rather than trying to provide ready-made production-quality implementations as Numerical Recipes does, it instead concentrates…
on “Why There Is No Hitchhiker’s Guide to Mathematics for Programmers” ↗Use a Pseudoinverse or a decomposition instead. A great book to read is Matrix Computations by Golub/van Loan.
on “Don’t invert that matrix (2010)” ↗It's standard LA fare... Pretty much any LA textbook will cover these. For a focus actual computation (ie numerical LA), consider Golub's (RIP) Matrix Computations (more of a reference, though, not so much for self-study), Trefethen's Numerical Linear Algebra, Demmel's Applied Numerical Linear Algebra.
on “Help Advance the World with Advanced Linear Algebra” ↗