Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB (2nd Edition) 2nd Edition by Charles F. Van Loan (PDF)

Description

Unique in content and approach, this book covers all the topics that are usually covered in an introduction to scientific computing–but folds in graphics and matrix-vector manipulation in a way that gets readers to appreciate the connection between continuous mathematics and computing. MATLAB 5 is used throughout to encourage experimentation, and each chapter focuses on a different important theorem–allowing readers to appreciate the rigorous side of scientific computing. In addition to standard topical coverage, each chapter includes 1) a sketch of a “hard” problem that involves ill-conditioning, high dimension, etc.; 2)at least one theorem with both a rigorous proof and a “proof by MATLAB” experiment to bolster intuition; 3)at least one recursive algorithm; and 4)at least one connection to a real-world application. The book revolves around examples that are packaged in 200+ M-files, which, collectively, communicate all the key mathematical ideas and an appreciation for the subtleties of numerical computing. Power Tools of the Trade. Polynomial Interpolation. Piecewise Polynomial Interpolation. Numerical Integration. Matrix Computations. Linear Systems. The QR and Cholesky Factorizations. Nonlinear Equations and Optimization. The Initial Value Problem. For engineers and mathematicians.

User’s Reviews

Editorial Reviews: From the Back Cover Unique in content and approach, this piece covers all the topics that are usually covered in an introduction to scientific computing—but folds in graphics and matrix-vector manipulation in a way that gets readers to appreciate the connection between continuous mathematics and computing. Matlab 5 is used throughout to encourage experimentation, and each chapter focuses on a different important theorem—allowing users to appreciate the rigorous side of scientific computing. In addition to standard topical coverage, each chapter includes 1) a sketch of a “hard” problem that involves ill-conditioning, high dimension, etc.; 2) at least one theorem with both a rigorous proof and a “proof by MATLAB” experiment to bolster intuition; 3) at least one recursive algorithm; and 4) at least one connection to a real-world application.FEATURES/BENEFITSNEW—Upgraded to a MATLAB 5 level.NEW—Approximately 60 new problems.,NEW—New sections on structure arrays, cell arrays, and how to produce more informative plots (Ch. 1).NEW—A brief treatment of trigonometric interpolation (Ch. 2)—A follow-up FFT solution to the problem is provided in Ch. 5). NEW—A brief discussion of sparse arrays (Ch. 5). Permits a limited study of sparse methods for linear equations and least squares in Chs. 6 and 7.NEW—Block matrix material—Now enriched with the use of cell arrays (Chs. 6-7).NEW—Orbit problem solutions—Now make use of simple structures (Ch. 8).Simplifies the presentation.NEW—More detailed coverage of “ode23” (Ch. 9).NEW—Website—Provides solutions to half the problems.Additional coverage of graphics.Numerical linear algebra—Permeates the entire presentation, beginning in Ch. 1. (This is a get-started-with-MATLAB tutorial, but is driven by examples that set the stage for the numerical algorithms that follow.)One important theorem covered per chapter.Motivational examples and related homework problems using MATLAB.Allows users to get a personal feel for algorithm strengths and weaknesses without the distraction of debugging the syntax of a compiled higher level language.An abundance of examples, packaged in 200+ M-files—The book revolves around examples that are packaged in 200+ M-files, which, collectively, communicate all the key mathematical ideas and an appreciation for the subtleties of numerical computing.Snapshots of advanced computing—In sections that deal with parallel adaptive quadrature and parallel matrix computations. Treatment of recursion includes divided differences, adaptive approximation, quadrature, the fast Fourier transform, Strassen matrix multiplication, and the Cholesky factorization. About the Author Charles F. Van Loan has been at Cornell University since 1975, where he is a Professor of Computer Science and the Joseph C. Ford Professor of Engineering. He is a SIAM Fellow and the author of Matrix Computations (with G. H. Golub; Johns Hopkins, 1996), Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB (Prentice Hall, 1999), Computational Frameworks for the Fast Fourier Transform (SIAM, 1992), Handbook for Matrix Computations (with T. F. Coleman; SIAM, 1988), and Introduction to Computational Science and Mathematics (James and Bartlett, 1996).

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Title leaves a lot to expect and doesn’t live up to it. I was looking for ways to optimize overdetermined systems and minimizing noise, also for numerical solves of non linear systems. It had a basic mat lab primer and a few trivial examples. Not worth it.

⭐The book was delivered on time and was in perfect shape. You can’t expect more than that, which is why I gave it 5 stars.

⭐I bought this book as a textbook for a course. Let’s just say I shouldn’t have bothered with it.

⭐Professor Van Loan provides a comprehensive text in the computational aspects of linear algebra, and his choice to include an explanation of computational methods with vectors and matrices within the context of Matlab offers students a clearer insight into how computetrs deal with linear algebra. A careful reader will be enlightened by algorithms which greatly increase computational efficiency. However, the book has its share of typos which can confuse people trying to understand the various Matlab scripts. I found that the chapter dealing with splines was extremely hard to understand without supplemental information. I would have like to seen more consistency as far as complexity analyses; while some algorithms provided clear runtime analyses, others did not. Also, some scripts could have been accompanied by a clearer explanation; it is often not intuitive how the writer got from the algorithm to actual code. All in all, by discussing computational methods in matrix-vector and matrix-matrix operations and linear system solving, this book both advances and enhances the reader’s linear algebra knowledge and also provides instruction on how computers perform most optimally and efficiently. A must-read for any serious undergraduate student of computational science, but perhaps not for those without a firm grasp on college mathematics.

⭐This is a well written introduction to scientific computing. It is not written for the professional, the graduate student, or the advanced undergraduate. Rather, this book is aimed at the lower division undergraduate who possesses a basic knowledge of calculus, linear algebra, programming. In that context it is clear, interesting, and well presented.

⭐This book invites the reader to build exploratory environments with MATLAB in which various mathematical experiments can be performed. Very interesting examples are investigated and good exercises are presented. I was amazed to see negative reviews and poor ratings. Yes, there are a few typos and little errors. But these should not stumble a serious student. A person who follows the book, builds the environments, experiments with the programs and the mathematics will learn a great deal.

⭐boolean HaveATestTomorrow, DoIUnderstandWhatLoanIsTryingToSay; HaveATestTomorrow = true; int timeTillTestinSeconds = 600; while(HaveATestTomorrow) { DoIUnderstandWhatLoanIsTryingToSay = false; timeTillTestinSeconds–; } // sigh

⭐This is probably the worst book in Scientific computation. This book doesnot explain any topic in depth. It’s a waste of money to buy this book.

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