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The second
edition of the author’s acclaimed textbook covers the major topics of
computational linear algebra, including solution of a system of linear
equations, least-squares solutions of linear systems, and computation of
eigenvalues, eigenvectors, and singular value problems.
The important features of the original edition have been updated and improved in the second edition:
• The
author covers a variety of motivating applications drawn from numerous
disciplines of science and engineering. When a physical problem is
posed, the scientific and engineering significance of the solution is
clearly stated.
• Each chapter contains a summary of the important
concepts developed in that chapter, suggestions for further reading, and
numerous exercises, both theoretical and MATLAB® and MATCOM based. The
author also provides a list of key words for quick reference.
• The
MATLAB® toolkit MATCOM contains implementations of the major algorithms
associated with the book and enables students to study different
algorithms for the same problem, comparing efficiency, stability, and
accuracy.
• The topics of generalized and quadratic eigenvalue
problems, which arise in practical engineering applications, are
described in great detail. This feature, along with an important
overview of Krylov subspace methods and an extensively updated
bibliography, enhances the book’s value as a reference for both
engineers and students.
This book is intended for
undergraduate and postgraduate students in applied and computational
mathematics, scientific computing, computer science, financial
mathematics, actuarial sciences, and electrical and mechanical
engineering.
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Preface
1. Linear Algebra Problems, Their Importance, and Computational Difficulties
2. A Review of Some Required Concepts from Core Linear Algebra
3. Floating Point Numbers and Errors in Computations
4. Stability of Algorithms and Conditioning of Problems
5. Gaussian Elimination and LU Factorization
6. Numerical Solutions of Linear Systems
7. QR Factorization, Singular Value Decomposition, and Projections
8. Least-Squares Solutions to Linear Systems
9. Numerical Matrix Eigenvalue Problems
10. Numerical Symmetric Eigenvalue Problem and Singular Value Decomposition
11. Generalized and Quadratic Egenvalue Problems
12. Iterative Methods for Large and Sparse Problems: An Overview
13. Some Key Terms in Numerical Linear Algebra
Bibliography
Index |
