Scientific Computing

This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results. In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.

Table of Contents

1 Scientific Computing

2 Systems of Linear Equations

3 Linear Least Squares

4 Eigenvalue Problems

5 Nonlinear Equations

6 Optimization

7 Interpolation

8 Numerical Integration and Differentiation

9 Initial Value Problems for ODEs

10 Boundary Value Problems for ODEs

11 Partial Differential Equations

12 Fast Fourier Transform

13 Random Numbers and Simulation

About the Author

Michael T. Heath is professor and Fulton Watson Copp Chair Emeritus in the department of computer science at the University of Illinois at Urbana-Champaign. His research interests are in scientific computing, particularly numerical linear algebra and optimization, and in parallel computing. He is a SIAM Fellow, ACM Fellow, Associate Fellow of the AIAA, and a member of the European Academy of Sciences. Professor Heath has received numerous teaching awards, including the Taylor L. Booth Education Award from the IEEE Computer Society.