Numerical Linear Algebra / William Layton & Mike Myron Sussman

"Many students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Each topic is presented as algorithmic ideas and through a foundation based on mostly applied analysis. By picking a path through the book appropriate for the level, it has been used for both senior level undergraduates and beginning graduate classes with students from diverse fields and backgrounds"-- Provided by publisher

TABLE OF CONTENTS
Introduction
Linear systems and finite precision arithmetic
Gaussian elimination
Norms and error analysis
The MPP and the curse of dimensionality
Iterative methods
Solving Ax = b by optimization
The conjugate gradient method
Elgenvalue problems
Appendix A; An omitted proof
Appendix B: Tutorial on basic MATHLAB programming