Numerical Linear Algebra with Applications: Using MATLAB and Octave, Second Edition provides practical knowledge on modern computational techniques for the numerical solution of linear algebra problems. The book offers a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions. Useful to readers regardless of background, the text begins with six introductory courses to provide background for those who haven’t taken applied or theoretical linear algebra. This approach offers a thorough explanation of the issues and methods for practical computing using MATLAB as the vehicle for computation.
Appropriate for advanced undergraduate and early graduate courses on numerical linear algebra, this useful textbook explores numerous applications to engineering and science.
Table of Contents
1. Matrices
2. Linear equations
3. Subspaces
4. Determinants
5. Eigenvalues and eigenvectors
6. Orthogonal vectors and matrices
7. Vector and matrix norms
8. Floating point arithmetic
9. Algorithms
10. Conditioning of problems and stability of algorithms
11. Gaussian elimination and the LU decomposition
12. Linear system applications
13. Important special systems
14. Gram-Schmidt decomposition
15. The singular value decomposition
16. Least-squares problems
17. Implementing the QR factorization
18. The algebraic eigenvalue problem
19. The symmetric eigenvalue problem
20. Basic iterative methods
21. Krylov subspace methods
22. Large sparse eigenvalue problems
23. Computing the singular value decomposition
Authors
William Ford University of the Pacific, Stockton, California, USA.William Ford completed his undergraduate degree at MIT, having majored in mathematics and minored in electrical engineering. He went on to complete a Ph.D. in mathematics at the University of Illinois, Urbana-Champaign, with his thesis paper entitled "Numerical Solution of Pseudo-parabolic Partial Differential Equations," and after two years of researching and teaching within the Department of Mathematics at Clemson University he joined the faculty of the Mathematics Department at the University of the Pacific, in Stockton, California. Here he went on to become a founding member of the Department of the Computer Science. Beginning in the 1980s, he and William Topp began jointly publishing books, that included a Motorola 68000 assembly language book through D.C. Heath, a book on data structures with C++ through Prentice Hall, and a book on data structures with Java through Prentice Hall. Dr. Ford additionally developed an IDE (Integrated Development Environment) named "EZJava" to accompany the Java book and served as the Chair of the Computer Science Department until his retirement in 2014.
David Stapleton Professor, Department of Mathematics & Statistics University of Central Oklahoma Edmond, Oklahoma, USA.David Stapleton received his BS from the University of California, Santa Barbara and MS from the University of California, San Diego, before earning his PhD from University of Arizona in 1990. Now a Professor at University of Central Oklahoma, Dr. Stapleton has taught courses in advanced calculus for applications, mathematical modeling, calculus of variations, tensors, numerical linear algebra, and other mathematical topics and has served three times as the Director of the Conference on Applied Mathematics. He has published articles in various journals and proceedings of the AIAA, SIAM, IEEE/ION PLANS, Navigation, Foundations of Physics, Physics Communications, AJCM, STAIF, FAA, ICAO, and more. He has also worked as a contractor to the FAA at the FAA Technical Center and Mike Monroney Aeronautical Center and also has experience as a contractor to the USAF at Cape Canaveral, Vandenberg AFB (now Vandenberg SFB), and Edwards AFB.
