The Conjugate Gradient Method Song

(to the tune of "My Bonnie Lies over the Ocean")

The conjugate gradient Method
is for matrices s.p.d.
And the conjugate gradient method
directly solves A x is b!

CHORUS:
Conjugate means A-orthogonal
and gradient's steepest descent, descent!
If only I could remember this,
I'd always know what CG meant.

The method has virtues aplenty:
Minimum residual's the first.
Convergence in number of eigenvalues,
And a three term recurrence.
CHORUS

The number of distinct eigenvalues
is how many steps it will run,
so the number of steps for I
would be a grand total of one!
CHORUS

The error at any step k
is guaranteed minimal;
over the subspace of Krylov
Nothing can be smaller at all.
CHORUS

"The Conjugate Gradient Method Song" Copyright (c) 2000-2007 Rebecca Hartman-Baker.

Last updated January 22, 2007
hartmanbakrj@ornl.gov