Diagonal differential operators

Corresponding to every differential operator exist a diagonal operator. Let op be a differential operator. Then, the corresponding diagonal operator is:

op.diag(a)

The return value of a diagonal differential operator is a vector representing the diagonal of the differential operator. The diagonal differential operator is helpful for the construction of a Gauss-Seidel relaxation.

Example:

A Gauss Seidel algorithm can be implemented as follows:i

     u = u - (op(u) -f) / op.diag();
 

Handbook

Last modified: Tue Feb 22 15:23:14 MET 2000