> El 17 feb 2020, a las 19:19, Emmanuel Ayala <[email protected]> escribió: > > Thank you very much for the answer. > > This error appears when computing the B-norm of a vector x, as sqrt(x'*B*x). > Probably your B matrix is semi-definite, and due to floating-point error the > value x'*B*x becomes negative for a certain vector x. The code uses a > tolerance of 10*PETSC_MACHINE_EPSILON, but it seems the rounding errors are > larger in your case. Or maybe your B-matrix is indefinite, in which case you > should solve the problem as non-symmetric (or as symmetric-indefinite GHIEP). > > Do you get the same problem with the Krylov-Schur solver? > > > After check the input matrices, the problem was solved using GHIEP. > > A workaround is to edit the source code and remove the check or increase the > tolerance, but this may be catastrophic if your B is indefinite. A better > solution is to reformulate the problem, solving the matrix pair (A,C) where > C=alpha*A+beta*B is positive definite (note that then the eigenvalues become > lambda/(beta+alpha*lambda)). > > > Ok, there is a rule to choose the values for alpha and beta?
For instance take alpha=1 and beta=-sigma, where sigma is a lower bound of the leftmost eigenvalue of B (the most negative one). This assumes that A is positive definite. Jose > > Kind regards. > Thanks. > >
