Is there any ojAlgo solver for when the condition number is large and the matrix is symmetric and indefinite?

Question

I use ojAlgo to solve a system of linear equations. In one case I get a RecoverableCondition exception. Probably because matrix is ill-conditioned, the condition number is about 1e15.

I use ojAlgo to solve it as seen in the code below. It usually works, but not in this case.

Is there any other solver I could use for a symmetric indefinite (ill-conditioned) matrix?

The present failing size is 18x18 but later 1000x1000 might be needed. Since its part of a iterative algorithm the accuracy is not super important.

         SolverTask<Double> equationSolver = SolverTask.PRIMITIVE.make(KKT, rhs.negate());
         MatrixStore<Double> deltaX = null;
         try {
            deltaX = equationSolver.solve(KKT, rhs.negate());
         } catch (RecoverableCondition ex) {
            int i = 0;
         }

I tried to reproduce this in a self contained example but failed, because there it works. Maybe I do not get exactly the same matrix down to the last bit.

Answer 1

In your case, that method would use a Cholesky decomposition as the solver.

If here's a problem then try to pick another decomposition by instantiating a suitable alternative directly. An SVD can usually handle anything, but that would be very expensive. Perhaps QR can be ok.

QR<Double> qr = QR.PRIMITIVE.make(templateBody);
qr.decompose(body);
qr.getSolution(rhs,x);

This way you can reuse the decomposition instance as well as the solution vector x.

Another alternative is to precondition the body/KKT matrix. Perhaps add a small diagonal - just enough to make the Cholesky decomposition solvable.

if (!cholesky.isSolvable()) {
    // Fix that
}

Or perhaps try something in the org.ojalgo.matrix.task.iterative package.