Solving linear system of equations in Lp

reverently intoned up the aether:

Quote:

> Hi-

> Is there a numerical method for minimizing Ax=b in Lp.

> I mean I want to minimize over x, ||Ax-b||^p.

> I guess conjugate gradient can be used here but I don't know how.

> I would greatly appreciate any help.

> Thanks,

> V

Try the course notes at the following link:

http://www.math.washington.edu/~burke/crs/516/

These notes should be reasonably up to date and if you can work

through them you will be ready to wander out and read the latest

journal articles on the subject.

A simple introduction to theory can be found in the course notes at:

http://www.math.washington.edu/~burke/crs/515/

The only change you are making here is to shift from working with a

quadratic function ||Ax-b|| to some other polynomial which may not be

as well behaved. i.e., p=1 (mod 2) implies that your objective is no

longer twice continuously differentiable as there may be a sharp

corner in you function near the zero(s).

enjoy,

Sean

"In the End, we will remember not the words of our enemies,

but the silence of our friends."

- Martin Luther King Jr. (1929-1968)