On 4/18/24 12:06, Tao Jin wrote:
I am developing a quasi Newton solver in deal.ii. During each iteration, I
need to solve a linear system B * x = p, where the matrix B has the following
form:
B = B_0 + W * M * W^T.
B_0 is an n by n sparse matrix (n is large > 100k);
M is a m by m *full matrix* (m is small m = 20 for example);
W is a n by m full matrix;
Since W * M * W^T will be an n by n fully dense matrix, I cannot afford to
explicitly store it.
Does the deal.ii community have any suggestion what is the most efficient way
to solve this linear system? I am thinking to use LinearOperator to define and
operate on W * M * W^T, but I am not sure whether it supports full matrix and
how efficient it would be.
Tao:
I'm not an expert in the LinearOperator framework, but operators such as yours
appear, for example, in step-20:
https://dealii.org/developer/doxygen/deal.II/step_20.html#step_20-Implementationoflinearsolversandpreconditioners
There, opS has exactly the form you describe, and it does not actually compute
the entries of the S matrix, but only represents the *action* as three
matrix-vector products.
That only leaves the question of whether you can use linear_operator(M) on
full matrices M. I don't know the answer to that, but what happens if you try?
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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