An Introduction to the Conjugate Gradient Method
Without the Agonizing Pain
(Edition 1 1/4)
Jonathan Richard Shewchuk
School of Computer Science
Carnegie Mellon University
Pittsburgh, Pennsylvania 15213
The Conjugate Gradient Method is the most prominent iterative method for
solving sparse systems of linear equations. Unfortunately, many textbook
treatments of the topic are written with neither illustrations nor intuition,
and their victims can be found to this day babbling senselessly in the corners
of dusty libraries. For this reason, a deep, geometric understanding of the
method has been reserved for the elite brilliant few who have painstakingly
decoded the mumblings of their forebears. Nevertheless, the Conjugate Gradient
Method is a composite of simple, elegant ideas that almost anyone can
understand. Of course, a reader as intelligent as yourself will learn them
almost effortlessly.
The idea of quadratic forms is introduced and used to derive the methods of
Steepest Descent, Conjugate Directions, and Conjugate Gradients. Eigenvectors
are explained and used to examine the convergence of the Jacobi Method,
Steepest Descent, and Conjugate Gradients. Other topics include
preconditioning and the nonlinear Conjugate Gradient Method. I have taken
pains to make this article easy to read. Sixty-two illustrations are
provided. Dense prose is avoided. Concepts are explained in several
different ways. Most equations are coupled with an intuitive interpretation.
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Classroom Figures for the Conjugate Gradient Method
Without the Agonizing Pain
(Edition 1 1/4)
Jonathan Richard Shewchuk
This report contains a set of full-page figures designed to be used as
classroom transparencies for teaching from the article ``An Introduction to
the Conjugate Gradient Method Without the Agonizing Pain''.
UNPUBLISHED DRAFT. PostScript (1409k).
Paper available by anonymous FTP to WARP.CS.CMU.EDU in directory quake-papers/
as the file painless-conjugate-gradient-figs.ps, or through the URL
http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient-figs.ps