Introduction To Scientific Computing: A Matrix-Vector Approach Using MATLAB (The Matlab Curriculum Series) - Softcover

Über die Autorin bzw. den Autor

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).

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Unique in content and approach, this piece 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 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 theoremallowing 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/BENEFITS

• 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 (Ch. 5).
  • Permits a limited study of sparse methods for linear equations and least squares in Chs. 6 and 7.
• NEWBlock matrix materialNow enriched with the use of cell arrays (Chs. 6-7).
• NEWOrbit problem solutionsNow make use of simple structures (Ch. 8).
  • Simplifies the presentation.
• NEWMore detailed coverage of "ode23" (Ch. 9).
• NEWWebsiteProvides solutions to half the problems.
  • Additional coverage of graphics.
• 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.)
• 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-filesThe 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 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.