Fundamentals of Matrix Computations / Wiley Series in Pure and Applied Mathematics (PDF)

A significantly revised and improved introduction to a critical
aspect of scientific computation

Matrix computations lie at the heart of most scientific
computational tasks. For any scientist or engineer doing
large-scale simulations, an understanding of the topic is
essential. Fundamentals of Matrix Computations, Second Edition
explains matrix computations and the accompanying theory clearly
and in detail, along with useful insights.

This Second Edition of a popular text has now been revised and
improved to appeal to the needs of practicing scientists and
graduate and advanced undergraduate students. New to this edition
is the use of MATLAB for many of the exercises and examples,
although the Fortran exercises in the First Edition have been kept
for those who want to use them. This new edition includes:

* Numerous examples and exercises on applications including
electrical circuits, elasticity (mass-spring systems), and simple
partial differential equations

* Early introduction of the singular value decomposition

* A new chapter on iterative methods, including the powerful
preconditioned conjugate-gradient method for solving symmetric,
positive definite systems

* An introduction to new methods for solving large, sparse
eigenvalue problems including the popular implicitly-restarted
Arnoldi and Jacobi-Davidson methods

With in-depth discussions of such other topics as modern
componentwise error analysis, reorthogonalization, and rank-one
updates of the QR decomposition, Fundamentals of Matrix
Computations, Second Edition will prove to be a versatile companion
to novice and practicing mathematicians who seek mastery of matrix
computation.