the conjugate gradient method
There are three paradigms for engineering numerical software,
we can use a library like
LAPACK,
or a scientific software system like
MATLAB,
Octave or
SciLab.
The third way is to use a toolkit, which provides templates to
create complicated algorithms from basic building blocks.
As an example, we sketched the layered structure of
PETSc,
which contains Krylov subspace methods to numerically solve PDEs
on parallel computers.
The main part of this lecture was devoted to sketching another class
of iterative solvers of linear systems, the so-called Krylov subspace
methods, and in particular for symmetric positive definite matrices
we looked at the conjugate gradient method.
Bibliography
- James W. Demmel: "Applied Numerical Linear Algebra", SIAM 1997.
- Jack Dongarra, Iain S. Duff, Danny C. Sorensen,
and Henk A. van der Vorst:
"Solving Linear Systems on Vector and Shared Memory Computers",
SIAM 1991.