Dear Wolfgang, I am glad to report that the LinearOperator modules also work for fully dense and non-rectangular matrices (FullMatrix<double>). I can now use the inverse operator to solve the linear system: B = B_0 + W * M * W^T. B_0 is an n by n sparse symmetric positive-definite 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;
Thanks again for your advice. Best, Tao On Saturday, April 20, 2024 at 12:27:02 AM UTC-4 Tao Jin wrote: > Dear Wolfgang, > > Thanks for the advice! > Best, > > Tao > > On Friday, April 19, 2024 at 11:58:33 PM UTC-4 Wolfgang Bangerth wrote: > >> On 4/19/24 21:54, Tao Jin wrote: >> > >> > Now that my LinearOperator is defined as B_0 + W * M * W^T, I only need >> to >> > find an appropriate iterative solver that can solve the inverse of this >> > operator (the underlying matrix is fully dense) efficiently. >> >> It is entirely unimportant that the matrix is dense. For iterative >> solvers, >> this is of no consequence at all. What matters is whether, for example, >> it is >> symmetric and/or positive definite. The other things that matters is >> whether >> you can construct a good preconditioner for it. >> >> You really should read through step-20 and step-22 to see how all of this >> works in practice. >> >> Best >> W. >> >> -- >> ------------------------------------------------------------------------ >> Wolfgang Bangerth email: [email protected] >> www: http://www.math.colostate.edu/~bangerth/ >> >> >> -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/cce59280-c6f2-428b-97ce-9335b78bf90fn%40googlegroups.com.
