My problem needs to solve dense symmetric linear systems something like:
A x = b,
A y = x,
A z = y+x,...in sequence.
In Eigen C++, if I take advantage of the symmetry of
A by using:
x=A.ldlt().solve(b); y=A.ldlt().solve(x); z=A.ldlt().solve(y+x);
The same matrix
A has to be
Cholesky factorized many times.
Similar issue may exists for
How can I reuse the coefficient matrix decomposition result for other systems?
It seems this is equivalent to ask whether there is a simple back-substitution solver for upper triangular linear systems.