
Introduction to Scientific Computing: A MatrixVector Approach Using MATLAB, 2/e
Charles F. Van Loan, Cornell University
Published July, 1999 by Prentice Hall Engineering/Science/Mathematics
Copyright 2000, 367 pp.
Paper
ISBN 0139491570

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For onesemester courses in Numerical Methods in computer
science and engineering programs, and Numerical Analysis courses in
mathematics programs.
Unique in content and approach, this text covers all the topics
that are usually covered in an introduction to scientific computing—but
folds in graphics and matrixvector manipulation in a way that gets
students 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 students 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 illconditioning,
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 realworld application. The text is brief and clear enough for
introductory numerical analysis students to “get their feet wet,”
yet comprehensive enough in its treatment of problems and applications
for higherlevel students to develop a deeper grasp of numerical tools.
NEW—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 followup 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. 67).
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 getstartedwithMATLAB
tutorial, but is driven by examples that set the stage for the numerical
algorithms that follow.)
One important theorem covered per chapter.
 Allows students to appreciate the rigorous side of scientific
computing.
Motivational examples and related homework problems
using MATLAB.
 Allows students 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+ Mfiles—The
text revolves around examples that are packaged in 200+ Mfiles, which,
collectively, communicate all the key mathematical ideas and an appreciation
for the subtleties of numerical computing. They also illustrate many
features of MATLAB that are likely to be useful later on in students'
careers.
 Provides students with a variety of handson opportunities
and gives instructors great flexibility in structuring assignments.
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.
1. Power Tools of the Trade.
2. Polynomial Interpolation.
3. Piecewise Polynomial Interpolation.
4. Numerical Integration.
5. Matrix Computations.
6. Linear Systems.
7. The QR and Cholesky Factorizations.
8. Nonlinear Equations and Optimization.
9. The Initial Value Problem.
Bibliography.
Index.
