- Paperback: 373 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: 37 customer reviews
- Amazon Best Sellers Rank: #378,353 in Books (See Top 100 in Books)
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Numerical Linear Algebra 1st Edition
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I have used Numerical Linear Algebra in my introductory graduate course and I have found it to be almost the perfect text to introduce mathematics graduate students to the subject. I like the choice of topics and the format: a sequence of lectures. Each chapter (or lecture) carefully builds upon the material presented in previous chapters, providing new concepts in a very clear manner. Exercises at the end of each chapter reinforce the concepts, and in some cases introduce new ones. …The emphasis is on the mathematics behind the algorithms, in the understanding of why the algorithms work. …The text is sprinkled with examples and explanations, which keep the student focused. --Daniel B. Szyld, Department of Mathematics, Temple University.
Just exactly what I might have expected--an absorbing look at the familiar topics through the eyes of a master expositor. I have been reading it and learning a lot. --Paul Saylor, University of Illinois at Urbana-Champaign
This is a beautifully written book which carefully brings to the reader the important issues connected with the computational issues in matrix computations. The authors show a broad knowledge of this vital area and make wonderful connections to a variety of problems of current interest. The book is like a delicate soufflé --- tasteful and very light. --Gene Golub, Stanford University.
This is a concise, insightful introduction to the field of numerical linear algebra. The authors' clear, inviting style and evident love of the field, along with their eloquent presentation of the most fundamental ideas in numerical linear algebra, make it popular with teachers and students alike.
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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.
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.
-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.