  At the heart of many scientific applications is the solution of algebraic
systems, such as linear systems of equations, eigenvalue problems, and
optimization problems, to name a few. TOPS, which stands for Towards Optimal
Petascale Simulations, is a SciDAC applied math center focused on the
development of solvers for tackling these algebraic systems, as well as the
deployment of such technologies in large-scale scientific applications of
interest to the U.S. Department of Energy. In this paper, we highlight some of
the solver technologies we have developed in optimization and matrix
computations. We also describe some accomplishments achieved using these
technologies in UNEDF, a SciDAC application project on nuclear physics.
