On Wed, Sep 21, 2016 at 10:20 PM, Munson, Todd <[email protected]> wrote:
> > You can set up TAO to solve such a problem. > > However, your problem boils down to solving the > linear system > > w - V*lambda = 0 > V'*w = b > > Taking the Schur complement with respect to w, you get > the system > > V'*V*lambda = b > > You then form and invert V'*V, which is a 5x5 matrix > and recover w = V*lambda. > > That will get you the least 2-norm solution for your > underdetermined system. > Fantastic, this is is perfect for us, Thanks, > LSQR will solve the underdetermined system and give > you the least norm solution if you don't want to > do the matrix-matrix product and inverse. LSQR > may also be more stable. See > > http://web.stanford.edu/group/SOL/software/lsqr/ > > That site suggests using CRAIG in the underdetermined > case, but I don't know if CRAIG is implemented > in PETSc. > > Other norms are more difficult to obtain, but can > be done. One and infinity norms are recast as > linear programming problems. Matrix norms are > equality constrained quadratic programs. > p-norms with p >= 1 are convex > nonlinear programs. > > Todd. > > > On Sep 21, 2016, at 8:24 PM, Mark Adams <[email protected]> wrote: > > > > I thought least squares was for tall skinny (overdetermined) solves? I > have a short fat (5 x ~100) matrix to solve. > > > > On Wed, Sep 21, 2016 at 4:24 PM, Stefano Zampini < > [email protected]> wrote: > > Mark, > > > > You can use KSPLSQR > > > > Stefano > > > > > > Il 21 set 2016 11:21 PM, "Mark Adams" <[email protected]> ha scritto: > > I want to solve for w in V' w = b, where V is tall and skinny. So a > short fat matrix "solve". This is underdetermined. I would like to minimize > the two norm (or any norm) of w. This looks like an optimization problem, > would TAO do this? > > Mark > > > >
