Synopses & Reviews
This book provides a seamless approach to numerical algorithms, modern programming techniques and parallel computing. These concepts and tools are usually taught serially across different courses and different textbooks, thus observing the connection between them. The necessity of integrating these subjects usually comes after such courses are concluded (e.g., during a first job or a thesis project), thus forcing the student to synthesize what is perceived to be three independent subfields into one in order to produce a solution. The book includes both basic and advanced topics and places equal emphasis on the discretization of partial differential equations and on solvers. Advanced topics include wavelets, high-order methods, non-symmetric systems and parallelization of sparse systems. A CD-ROM accompanies the text.
'This book is a valuable addition to the literature on numerical algorithms.' Numerical Algorithms
'There is plenty of material for a two-semester sequence, or selected chapters could be used for a one-semester course on numerical linear algebra. The presentation is clear, practical, and lively ... this text would be a very useful reference for statistics students and professionals) seeking to take their statistical computing skills into the parallel realm.' Journal of the American Statistical Association
Includes bibliographical references (p. 607-610) and index.
This book provides a seamless approach to numerical algorithms, modern programming techniques, and parallel computing. Such concepts and tools are often taught serially across different courses and different textbooks, and hence the interconnection between them is not immediately apparent. The book includes both basic as well as advanced topics and places equal emphasis on the discretization of partial differential equations and on solvers. Some of the advanced topics include wavelets, high-order methods, non-symmetric systems and parallelization of sparse systems.
Table of Contents
1. Scientific computing and simulation science; 2. Basic concepts; 3. Approximations; 4. Roots and integrals; 5. Explicit discretizations; 6. Implicit discretizations; 7. Relaxation: discretization and solvers; 8. Propagation: numerical diffusion and dispersion; 9. Fast linear solvers; 10. Fast eigensolvers; Appendix A: C++ basics; Appendix B: MPI basics; Bibliography.