Demmel The purpose of this proposal is is design, analyze and make widely available massively parallel algorithms for large sparse linear systems, large sparse nonsymmetric eigenproblems,and large dense eigenproblems. Also proposed are new algorithms which are innovative numerically and with regard to their parallelizability. These algorithms will be packaged in toolboxes which permit their easy reuse and performance for a wide variety of applications too demanding for any "black box" solution.