Scientific Computing: An Introduction with Parallel Computing

Description

Introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. The book contains chapters on parallel and vector matrix multiplication and on the solution of linear systems by direct and iterative methods. Includes bibliographical references (pages 413-428) and indexes. Ch. 1. The World of Scientific Computing -- 1.1. What Is Scientific Computing? -- 1.2. Mathematical Modeling -- 1.3. The Process of Numerical Solution -- 1.4. The Computational Environment -- Ch. 2. Linear Algebra -- 2.1. Matrices and Vectors -- 2.2. Eigenvalues and Canonical Forms -- 2.3. Norms -- Ch. 3. Parallel and Vector Computing -- 3.1. Parallel and Vector Computers -- 3.2. Basic Concepts of Parallel Computing -- 3.3. Matrix Multiplication -- Ch. 4. Polynomial Approximation -- 4.1. Taylor Series. Interpolation and Splines -- 4.2. Least Squares Approximation -- 4.3. Application to Root-Finding -- Ch. 5. Continuous Problems Solved Discretely -- 5.1. Numerical Integration -- 5.2. Initial Value Problems -- 5.3. Boundary Value Problems -- 5.4. Space and Time -- 5.5. The Curse of Dimensionality -- Ch. 6. Direct Solution of Linear Equations -- 6.1. Gaussian Elimination -- 6.2. Errors in Gaussian Elimination -- 6.3. Other Factorizations -- Ch. 7. Parallel Direct Methods -- 7.1. Basic Methods -- 7.2. Other Organizations of Factorization -- 7.3. Banded and Tridiagonal Systems -- Ch. 8. Iterative Methods -- 8.1. Relaxation-Type Methods -- 8.2. Parallel and Vector Implementations -- 8.3. The Multigrid Method -- Ch. 9. Conjugate Gradient-Type Methods -- 9.1. The Conjugate Gradient Method -- 9.2. Preconditioning -- 9.3. Nonsymmetric and Nonlinear Problems