Numerical Linear Algebra and Applications

Full of features and applications, this acclaimed textbook for upper undergraduate level and graduate level students includes all the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems. Drawing from numerous disciplines of science and engineering, the author covers a variety of motivating applications. 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 available online, 'MATCOM', contains implementations of the major algorithms in the book and will enable students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy.

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 eigenvalue problems; 12. Iterative methods for large and sparse problems: an overview; 13. Key terms in numerical linear algebra; Bibliography; Index; Online materials; 14. Special topics; Appendix A. Some software for matrix computations; Appendix B. A brief introduction to MATLAB®; Appendix C. MATCOM and selected MATCOM commands; Appendix D. Partial solutions and answers to selected problems.

An undergraduate textbook that highlights motivating applications and contains summary sections, examples, exercises, online MATLAB codes and a MATLAB toolkit. All the major topics of computational linear algebra are covered, from basic concepts to advanced topics such as the quadratic eigenvalue problem in later chapters.