On 11/20/18 2:27 PM, 'Maxi Miller' via deal.II User Group wrote:
> how exactly can I understand that? I have to generate a second matrix, which
> then will be added to the sparse matrix, but (due to the vector
> multiplication) will be a full matrix, something I would like to avoid.
No, you don't generate a matrix. You just store the vectors. Let's say these
vectors are x_k and y_k and that the second matrix has the form
\sum_k y_k x_k^T
Then you implement the vmult function of your "matrix-like" class as
void BroydenOperator::vmult (Vector<double> &dst,
const Vector<double> &src) const
{
dst = 0;
for (unsigned int k=0; k<n_vectors; ++k)
{
const double xk_dot_src = x[k] * src;
dst.add (xk_dot_src, y[k]);
}
}
This implements the *action* of the matrix without ever storing the elements
of the matrix.
Take a look at step-20 or step-22 to say more examples of operators for which
we don't know the matrix entries.
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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