Scientific Computing with Case Studies

Häftad, Engelska, 2008

1 649 kr

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Learning through doing is the foundation of this book, which allows readers to explore case studies as well as expository material. The book provides 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 is emphasized, and the MATLAB® algorithms are grounded in sound principles of software design and in the understanding of machine arithmetic and memory management.Nineteen case studies allow readers to become familiar with mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. A website provides solutions to the challenges that are offered throughout the book and also supplies relevant MATLAB codes, derivations, and supplementary notes and slides.

Produktinformation

Utgivningsdatum2008-12-30
Mått152 x 229 x 17 mm
Vikt832 g
FormatHäftad
SpråkEngelska
Antal sidor399
FörlagSociety for Industrial & Applied Mathematics,U.S.
ISBN9780898716665

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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.

PrefacePart I: Preliminaries: Mathematical Modeling, Errors, Hardware, and SoftwareChapter 1: Errors and ArithmeticChapter 2: Sensitivity Analysis: When a Little Means a LotChapter 3: Computer Memory and Arithmetic: A Look Under the HoodChapter 4: Design of Computer Programs: Writing Your LegacyPart II: Dense Matrix ComputationsChapter 5: Matrix FactorizationsChapter 6: Case Study: Image Deblurring: I Can See Clearly NowChapter 7: Case Study: Updating and Downdating Matrix Factorizations: A Change in PlansChapter 8: Case Study: The Direction-of-Arrival ProblemPart III: Optimization and Data FittingChapter 9: Numerical Methods for Unconstrained OptimizationChapter 10: Numerical Methods for Constrained OptimizationChapter 11: Case Study: Classified Information: The Data Clustering ProblemChapter 12: Case Study: Achieving a Common Viewpoint: Yaw, Pitch, and RollChapter 13: Case Study: Fitting Exponentials: An Interest in RatesChapter 14: Case Study: Blind Deconvolution: Errors, Errors, EverywhereChapter 15: Case Study: Blind Deconvolution: A Matter of NormPart IV: Monte Carlo ComputationsChapter 16: Monte Carlo PrinciplesChapter 17: Case Study: Monte-Carlo Minimization and Counting One, Two, Too ManyChapter 18: Case Study: Multidimensional Integration: Partition and ConquerChapter 19: Case Study: Models of Infections: Person to PersonPart V: Ordinary Differential EquationsChapter 20: Solution of Ordinary Differential EquationsChapter 21: Case Study: More Models of Infection: It’s EpidemicChapter 22: Case Study: Robot Control: Swinging Like a PendulumChapter 23: Case Study: Finite Differences and Finite Elements: Getting to Know YouPart VI: Nonlinear Equations and Continuation MethodsChapter 24: Nonlinear SystemsChapter 25: Case Study: Variable-Geometry TrussesChapter 26: Case Study: Beetles, Cannibalism, and ChaosPart VII: Sparse Matrix Computations, with Application to Partial Differential EquationsChapter 27: Solving Sparse Linear Systems: Taking the Direct ApproachChapter 28: Iterative Methods for Linear SystemsChapter 29: Case Study: Elastoplastic Torsion: Twist and StressChapter 30: Case Studt: Fast Solvers and Sylvester Equations: Both Sides NowChapter 31: Case Study: Eigenvalues: Valuable PrinciplesChapter 32: Multigrid Methods: Managing Massive MeshesBibliographyIndex