by Ian Craw
Publisher: University of Aberdeen 2003
Number of pages: 156
The overall aim of the course is to present modern computer programming techniques in the context of mathematical computation and numerical analysis and to foster the independence needed to use these techniques as appropriate in subsequent work.
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by Kurt Mehlhorn, Chee Yap - New York University
Contents: Introduction to Geometric Nonrobustness; Modes of Numerical Computation; Geometric Computation; Arithmetic Approaches; Geometric Approaches; Exact Geometric Computation; Perturbation; Filters; Algebraic Background; Zero Bounds; etc.
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Stability estimates and resolvent conditions in the numerical solution of initial value problems. Contents: Partial differential equations and numerical methods; Linear algebra; Stability in the numerical solution of differential equations; etc.
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We start with finite-precision arithmetic. We then discuss how to solve ordinary differential equations and partial differential equations using the technique of separation of variables. We then introduce numerical time-stepping schemes...
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This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods.