The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing nonorthogonal basis functions for ab initio electronic structure calculations. In this paper, we propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative...

Active control methods have been applied to a number of practical problems in which it is necessary to control a tonal disturbance. For example, the control of engine noise and vibration in vehicles, propeller noise in aircraft and the vibration produced by reciprocating machinery in many industrial systems. In such applications the steepest-descent algorithm has been widely employed, in part d...

A new method is given for eeecting numerical diierentiation by means of an optimization procedure. The method is shown to be eeective for the diierentiation of noisy functions, and stability and convergence results for a steepest descent implementation are proved.

In this paper, we propose a simple set theoretic blind deconvolution scheme based on a recently developed convex projection technique called Hybrid Steepest Descent Methods. The scheme is essentially motivated by Kundur and Hatzinakos’s idea that minimizes a certain cost function uniformly reflecting all a priori information such that (i) nonnegativity of the true image and (ii) support size of...

We design and study an adaptive algorithm for the numerical solution of the stationary nonlinear Stokes problem. The algorithm can be interpreted as a disturbed steepest descent method, which generalizes Uzawa’s method to the nonlinear case. The outer iteration for the pressure is a descent method with fixed step-size. The inner iteration for the velocity consists of an approximate solution of ...