  We introduce a novel solver to significantly reduce the size of a geometric
operator while preserving its spectral properties at the lowest frequencies. We
use chordal decomposition to formulate a convex optimization problem which
allows the user to control the operator sparsity pattern. This allows for a
trade-off between the spectral accuracy of the operator and the cost of its
application. We efficiently minimize the energy with a change of variables and
achieve state-of-the-art results on spectral coarsening. Our solver further
enables novel applications including volume-to-surface approximation and
detaching the operator from the mesh, i.e., one can produce a mesh tailormade
for visualization and optimize an operator separately for computation.
