Computational Methods of Linear Algebra

This book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming problems. The book also includes a chapter on the fast Fourier transform and a very practical introduction to the solution of linear algebra problems on modern supercomputers.

The book contains the relevant theory for most of the methods employed. It also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs for solving linear algebraic problems. Highly readable FORTRAN and MATLAB codes are presented which solve all of the main problems studied.

Contents:

• Reference Material
• Systems of Linear Equations
• Linear Least Squares Problems
• The Eigenvalue Problem
• Linear Programming
• The Fast Fourier Transform
• Linear Algebra on Supercomputers

Readership: Undergraduate and graduate students, researchers in computational mathematics and linear algebra.
Key Features:

• The chapter on parallel algorithms is one of the best short and practical introductions to parallel programming available; students will see and write MPI-based Fortran programs which solve linear algebraic problems efficiently on parallel systems
• There is a chapter on linear programming — a topic not often covered in computational linear algebra books — which includes detailed discussions of duals, the revised simplex method and transportation problems, and touches on interior point methods as well
• There is a chapter on fast Fourier transforms, and this is also not often covered in computational linear algebra books