We propose and study a block-iterative projections method for solving linear equations and/or inequalities. The method allows diagonal component-wise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system, and is thus called diagonally-relaxed orthogonal projections (DROP). Diagonal relaxation has proven useful in accelerating the initial convergence...

We consider the solution of strongly monotone variational inequalities of the form F (x∗)′(x−x∗) ≥ 0, for all x ∈ X. We focus on special structures that lend themselves to sampling, such as when X is the intersection of a large number of sets, and/or F is an expected value or is the sum of a large number of component functions. We propose new methods that combine elements of incremental constra...

Current methods used for stochastic projection of the finances of the combined Old-Age and Survivors Insurance and Disability Insurance (OASDI) trust fund are described and found to have problems. Structural time series models and alternative Monte Carlo procedures are identified as new methods that may be able to solve these problems. The new methods are implemented using the productivity grow...

We introduce and study a new class of projection methods—namely, the velocitycorrection methods in standard form and in rotational form—for solving the unsteady incompressible Navier–Stokes equations. We show that the rotational form provides improved error estimates in terms of the H1-norm for the velocity and of the L2-norm for the pressure. We also show that the class of fractional-step meth...

This paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature on polynomial eigenproblems which take advantage of a linearization of the problem.

and K(s) = [ AK BK CK DK ] be an n κ order controller with transfer function K(s) = CK(sI − AK)−1BK + DK . We seek a reduced-order controller Kr(s) of order r with r nκ to replace K(s). Assume that both G(s) and K(s) are single-input single-output (SIS0), and that K(s) is a stable stabilizing controller. (The general case follows simply and will be presented in the full paper.) Requiring Kr(s) ...

We derive a general class of iteration schemes for the incompressible Navier{Stokes equations which contains fully coupled solution techniques as well as operator splitting/projection methods. We combine the advantages of both, namely accuracy/stability and eeciency, and obtain a special form of discrete projection schemes. In combination with a nonlinear iteration of quasi{Newton type one may ...

A systematic study of the pairing-correlations derived from various particle-number projection methods is performed in an exactly soluble cranked-deformed shell model Hamiltonian. It is shown that most of the approximate particle-number projection methods including the method of Lipkin-Nogami, which is used quite extensively in nuclear structure studies, breakdown in the weak pairing limit. The...

A surjective space transformation technique is used to convert an original dual linear programming problem with equality and inequality constraints into a problem involving only equality constraints. Continuous and discrete versions of the stable gradient projection method are applied to the reduced problem. The numerical methods involve performing inverse transformations. The convergence rate ...