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Scientific Computing with Case Studies

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Author: Dianne P. O'Leary, University of Maryland, College Park

Date Published: March 2009
availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
format: Paperback
isbn: 9780898716665

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This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.
- A practical guide that offers exercises throughout the book
- Includes nineteen case studies to allow readers to become familiar with mathematical modelling and algorithm design
- A supporting website supplies relevant MATLAB codes, derivations, and supplementary notes and slides
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Product details
- Date Published: March 2009
- format: Paperback
- isbn: 9780898716665
- length: 395 pages
- dimensions: 254 x 174 x 17 mm
- weight: 0.81kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
Preface
Part I. Preliminaries: Mathematical Modeling, Errors, Hardware, and Software
1. Errors and arithmetic
2. Sensitivity analysis: when a little means a lot
3. Computer memory and arithmetic: a look under the hood
4. Design of computer programs: writing your legacy
Part II. Dense Matrix Computations:
5. Matrix factorizations
6. Case study: image deblurring: I can see clearly now
7. Case study: updating and downdating matrix factorizations: a change in plans
8. Case study: the direction-of-arrival problem
Part III. Optimization and Data Fitting:
9. Numerical methods for unconstrained optimization
10. Numerical methods for constrained optimization
11. Case study: classified information: the data clustering problem
12. Case study: achieving a common viewpoint: yaw, pitch, and roll
13. Case study: fitting exponentials: an interest in rates
14. Case study: blind deconvolution: errors, errors, everywhere
15. Case study: blind deconvolution: a matter of norm
Part IV. Monte Carlo Computations:
16. Monte Carlo principles
17. Case study: Monte-Carlo minimization and counting one, two, too many
18. Case study: multidimensional integration: partition and conquer
19. Case study: models of infections: person to person
Part V. Ordinary Differential Equations:
20. Solution of ordinary differential equations
21. Case study: more models of infection: it's epidemic
22. Case study: robot control: swinging like a pendulum
23. Case study: finite differences and finite elements: getting to know you
Part VI. Nonlinear Equations and Continuation Methods:
24. Nonlinear systems
25. Case study: variable-geometry trusses
26. Case study: beetles, cannibalism, and chaos
Part VII. Sparse Matrix Computations with Application to Partial Differential Equations:
27. Solving sparse linear systems: taking the direct approach
28. Iterative methods for linear systems
29. Case study: elastoplastic torsion: twist and stress
30. Case study: fast solvers and Sylvester equations: both sides now
31. Case study: eigenvalues: valuable principles
32. Multigrid methods: managing massive meshes
Bibliography
Index.

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Author
Dianne P. O'Leary, University of Maryland, College Park
Dianne Prost O'Leary is a professor of computer science at the University of Maryland, and also holds an appointment in the university's Institute for Advanced Computer Studies (UMIACS) and in the Applied Mathematics and Scientific Computing Program. She earned a B.S. from Purdue University and a Ph.D. from Stanford University. Her research is in computational linear algebra and optimization, with applications to solution of ill-posed problems, image deblurring, information retrieval, and quantum computing. She has authored over 90 research publications on numerical analysis and computational science and 30 publications on education and mentoring.