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. 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 <mfad...@lbl.gov> 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 <stefano.zamp...@gmail.com> > wrote: > Mark, > > You can use KSPLSQR > > Stefano > > > Il 21 set 2016 11:21 PM, "Mark Adams" <mfad...@lbl.gov> 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 >
