Shewchuk: An Introduction to the Conjugate Gradient Method Without the Agonizing Pain

by Carson Reynolds

A errand to run before summarizing the article. We must find a good definition for conjugate. In the most general sense, the word seems to mean to unite or join. But there is a more particular mathematical sense:

Conjugate \Con”ju*gate\, a. [L. conjugatus, p. p. or conjugare
to unite; con- + jugare to join, yoke, marry, jugum yoke;
akin to jungere to join. See {Join}.]
1. United in pairs; yoked together; coupled.
[1913 Webster]
5. (Math.) Presenting themselves simultaneously and having
reciprocal properties; — frequently used in pure and
applied mathematics with reference to two quantities,
points, lines, axes, curves, etc.
[1913 Webster]

We then take conjugate to mean, in the context of this paper, the set of directions which are used to descend the gradient instead of the steepest decent method.