Computational Methods of Linear Algebra, 2nd Edition
The Second Edition of this popular textbook provides a highly accessible introduction to the numerical solution of linear algebraic problems. Readers gain a solid theoretical foundation for all the methods discussed in the text and learn to write FORTRAN90 and MATLAB(r) programs to solve problems. This new edition is enhanced with new material and pedagogical tools, reflecting the author's hands-on teaching experience, including:
* A new chapter covering modern supercomputing and parallel programming
* Fifty percent more examples and exercises that help clarify theory and demonstrate real-world applications
* MATLAB(r) versions of all the FORTRAN90 programs
* An appendix with answers to selected problems
The book starts with basic definitions and results from linear algebra that are used as a foundation for later chapters. The following four chapters present and analyze direct and iterative methods for the solution of linear systems of equations, linear least-squares problems, linear eigenvalue problems, and linear programming problems. Next, a chapter is devoted to the fast Fourier transform, a topic not often covered by comparable texts. The final chapter features a practical introduction to writing computational linear algebra software to run on today's vector and parallel supercomputers.
Highlighted are double-precision FORTRAN90 subroutines that solve the problems presented in the text. The subroutines are carefully documented and readable, allowing students to follow the program logic from start to finish. MATLAB(r) versions of the codes are listed in an appendix. Machine-readable copies of the FORTRAN90 and MATLAB(r) codes can be downloaded from the text's accompanying Web site.
With its clear style and emphasis on problem solving, this is a superior textbook for upper-level undergraduates and graduate students.
1. Systems of Linear Equations.
2. Linear Least-squares Problems.
3. The Eigenvalue Problem.
4. Linear Programming.
5. The Fast Fourier Transform.
6. Linear Algebra on Supercomputers.
Appendix A:MATLAB Programs.
Appendix B: Answers to Selected Exercises.
"The author's presentation in excellent, providing motivation to the student throughout...an excellent, extremely readable introduction to computational linear algebra…" (MAA Reviews, December 28, 2005)