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Numerical Linear Algebra
Download Numerical Linear Algebra
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This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra.
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Product details
Paperback: 184 pages
Publisher: SIAM: Society for Industrial and Applied Mathematics; 1 edition (June 1, 1997)
Language: English
ISBN-10: 0898713617
ISBN-13: 978-0898713619
Product Dimensions:
6 x 0.8 x 9 inches
Shipping Weight: 1.4 pounds (View shipping rates and policies)
Average Customer Review:
4.2 out of 5 stars
40 customer reviews
Amazon Best Sellers Rank:
#104,782 in Books (See Top 100 in Books)
This is without a doubt the most gentle treatment of not just algorithms and efficiency in numerical computations, but also the theory that allows these algorithms to work, and I really wish other books would follow suit. Too many books are more concerned with jamming ideas in your face over hundreds of topics because they fear becoming outdated in an ever expanding field (ESPECIALLY where linear algebra, or just vectors/data, is concerned).But this book has a clear purpose in mind. "This is a vector. A bunch of sorted data is a vector. This is how we need to handle it. This is how we're going to improve it. You can manipulate data like this, but not like that." And with that, you're left not just wanting more, but you're also fully prepared to tackle a more advanced text (like Iterative Methods for Sparse Linear Systems, an ideal "next step" from here. Or perhaps you're ready for linear programming/optimization methods? Or maybe even branching into nonlinear programming? Or convex analysis?). And you have the best foundation for being able to read through those jargon-heavy papers with giant summation signs and vector notation strewn everywhere without feeling "Oh, geez, another one of THESE papers."And this book, with all of its chapters and contents, is in no hurry to catch up with modern methods. It takes time to explain "Hey, look, we get that there are better ways of doing it. But the reasons those methods exist is because of what we're trying to show you."And the problems, wow! They're sorted into every possible category. You have your typical Simple - Challenging range, but you also have problems clearly designed for engineers with little abstract mathematical analysis ideas, problems clearly designed for computer scientists who have some knowledge but want something specifically applicable to them, problems clearly designed for the mathematician who can prove, and problems clearly designed for the mathematician who has more interest in application but needs more meat than the average engineer.And the presentation, wow! So much care is given to how much white space is needed between theorems, sections, equations, and algorithms. Trefethen and Bau know that math books, particularly numerical ones, tend to cram information too close together which can hurt the eyes.I'm absolutely gah-gah for this book. And you would be, too, if you sat down, read it, and worked through it. This is the second book I've ever had any desire to just sit down and try and work every problem through, and I'm almost done with it! And while there's only one book out there I frequently reread, this is one of the very books I keep coming back to when I need a quick reference while trying to sift through something like Bender's Decomposition or trying to construct a genetic algorithm.
This book is the best I have found for studying computational linear algebra. It is clearly written and well thought out. It might not be the best introduction to the subject, and something like Strang's Linear Algebra book is probably a better place to start out. The first few chapters are more of a review of an introductory linear algebra course, and assume that one has already seen standard topics like the definition of vector spaces, subspaces, spanning sets, linear independence, etc. However, for those who have taken a 1 quarter or semester course in linear algebra, this is the perfect place to go next.
Face it, most math textbooks are awful: boring to read, not much insight, little more than a compendium of definitions, theorems, proofs, and examples. Trefethen and Bau is an exception to that rule. Indeed, the field of numerical linear algebra is unusual in having available several top-notch textbooks: Golub and Van Loan, Stewart's two volumes, Saad's books on iterative methods, Demmel's introduction, Watkins' undergraduate level treatment, and T&B. All of these are excellent (and any student in numerical analysis should delve into all of them) but to my tastes T&B and Stewart are the standouts for insight and simply being fun to read.If you're a student using T&B in a course, to use it effectively you need to understand that T&B is a book to be read carefully for understanding; it's not a typical textbook suited only for "mining" for examples and solutions to homework problems. My students have sometimes complained -- accurately -- that T&B is short on details and worked examples, and many of the proofs are just sketches. But that's a feature, not a bug: you can learn much by filling in the missing steps. This is book for reading, so take the time to read it, to think about what you've read, and to fill in the gaps; it's worth it. If you need some worked examples, Watkins has them in great detail and would be a good supplement to T&B (though see the caveat below).The only minor gripe I have about T&B is that the order of topics (QR before LU before Cholesky) is unusual, which makes it a little awkward to coordinate with other books such as Watkins which do Cholesky before LU before QR.
I am a second year PhD student in Operations Research and for long I had been looking for a book in linear algebra to help me learn it myself (as I see that I need it no matter what research I want to do. It's just a good tool to know). One of my friends recommended this book to me, I got it and I am very happy with it. The book is great in different ways:-it is in the form of short lectures and for me who wants to learn linear algebra step by step, this is a perfect approach. You will have a 5-6 page lecture so whenever you start, you are set to finish that lecture.-It gives you intuition and understanding about what is really happenning geometrically which is amazing. To me, it is very important to have the "feeling" of what is happening because it is only then that you can think about bringing your real problem in this framework.-The examples in lectures clarify the subject while exercises give you a chance to learn even more.If you are new to linear algebra or know it but want to refresh your mind on intuitions and systematic thinking, I highly recommend this book.
Like this book a lot. I'm not a great mathematician so take this review with a grain of salt. But I had this book for a grad class and learned more computationally than I have in any other class.
Wonderful book, gives me a starting point for understanding most basic algorithms I come across as a user of linear algebra software.
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