  We introduce a new general purpose multiresolution preconditioner for
symmetric linear systems. Most existing multiresolution preconditioners use
some standard wavelet basis that relies on knowledge of the geometry of the
underlying domain. In constrast, based on the recently proposed Multiresolution
Matrix Factorization (MMF) algorithm, we construct a preconditioner that
discovers a custom wavelet basis adapted to the given linear system without
making any geometric assumptions. Some advantages of the new approach are fast
preconditioner-vector products, invariance to the ordering of the rows/columns,
and the ability to handle systems of any size. Numerical experiments on finite
difference discretizations of model PDEs and off-the-shelf matrices illustrate
the effectiveness of the MMF preconditioner.
