Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB, 2/e
Charles F. Van Loan, Cornell University
Published July, 1999 by Prentice Hall Engineering/Science/Mathematics
Copyright 2000, 367 pp.
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For one-semester courses in Numerical Methods in computer
science and engineering programs, and Numerical Analysis courses in
Unique in content and approach, this text covers all the topics
that are usually covered in an introduction to scientific computingbut
folds in graphics and matrix-vector 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
theoremallowing 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 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 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 higher-level students to develop a deeper grasp of numerical tools.
NEWUpgraded to a MATLAB 5 level.
NEWApproximately 60 new problems.
NEWNew sections on structure arrays,
cell arrays, and how to produce more informative plots (Ch. 1).
NEWA brief treatment of trigonometric
interpolation (Ch. 2)A follow-up FFT solution to the problem
is provided in Ch. 5).
NEWA brief discussion of sparse arrays
NEWBlock matrix materialNow
enriched with the use of cell arrays (Chs. 6-7).
- Permits a limited study of sparse methods for linear
equations and least squares in Chs. 6 and 7.
NEWOrbit problem solutionsNow
make use of simple structures (Ch. 8).
NEWMore detailed coverage of ode23
- Simplifies the presentation.
to half the problems.
Numerical linear algebraPermeates 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.)
- Additional coverage of graphics.
One important theorem covered per chapter.
Motivational examples and related homework problems
- Allows students to appreciate the rigorous side of scientific
An abundance of examples, packaged in 200+ M-filesThe
text 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. They also illustrate many
features of MATLAB that are likely to be useful later on in students'
- 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.
Snapshots of advanced computingIn 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.
- Provides students with a variety of hands-on opportunities
and gives instructors great flexibility in structuring assignments.
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.