Scientific Computing: An Introduction with Parallel Computing

by Gene H. Golub, James M. Ortega

This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case.

* Gives a modern overview of scientific computing including parallel an vector computation* Introduces numerical methods for both ordinary and partial differential equations* Has considerable discussion of both direct and iterative methods for linear systems of equations, including parallel and vector algorithms* Covers most of the main topics for a first course in numerical methods and can serve as a text for this course

442 pages, Hardcover

First published September 1, 1991

Reviews

[Tomáš Ševček · Rating 4 out of 5]

A good self-contained introduction to the numerical analysis of differential equations. The book covers standard topics such as initial value problems for ODEs, boundary value problems for ODEs and initial-boundary value problems for PDEs. The book is self-contained in the sense that it covers all the necessary material from numerical mathematics (numerical integration/quadrature, differences, numerical solutions of (non-)linear equations, etc.) and even useful matrix algorithms (QR, Householder and so on). However, while the book provides numerous methods for solving ODE problems, I find the parts on PDEs unsatisfactory since only the most basic approaches are covered (and only for the scalar case). Still, these methods are enough to solve most linear PDEs and non-linear PDEs with non-linearities in the source term (as they can be treated in the similar fashion to the ODE case). If you want to solve (systems of) non-linear PDEs with more difficult non-linearities, you will have to search for methods not covered in the book, such as operator splitting. There is also very little on finite elements and virtually nothing on finite volumes. Finite elements and Galerkin are covered in the part on boundary value problems for ODEs, but not in the PDE case (and their treatment is rather informal as a rigorous treatment would require a solid grasp of functional analysis). All in all, a good intro text, but not suitable if you want to learn more advanced techniques for solving PDEs numerically.