In these lectures, I will describe a simple iterative method that supplies new proofs of integrality of linear characterizations of various basic problems in combinatorial optimization, and also allows adaptations to design approximation algorithms for NP-hard variants of these problems involving extra “degree-like” budget constraints. It is inspired by Jain’s iterative rounding method for desi...

SUMMARY We present several preconditioned conjugate gradient methods for the iterative solution of the linear, symmetric systems of equations arising from the nite element method in displacement form, both for the h-version and the p-version. The preconditioners are based on a decomposition of the solution space into overlapping subspaces and solving separately on each subspace. A judicious cho...

Iterative methods based on small functions are used both to show local surjectivity of certain operators and a fixed point property of mappings on scales of complete metric spaces.

Although image restoration methods based on spectral filtering techniques are very efficient, they can be applied only to problems with fairly simple spatially invariant blurring operators. Iterative methods, however, are much more flexible; they can be very efficient for spatially invariant as well as spatially variant blurs, they can incorporate a variety of regularization techniques and boun...

In a previous paper, we introduced a coordinate-splitting (CS) form of the equations of motion for multibody systems which together with a modiied nonlinear iteration (CM), is particularly eeective in the solution of certain nonlinear highly oscillatory systems. In this paper, we examine the convergence of the CS and CM iterations and explain the improved convergence of the CM iteration. An exa...

The purpose of the paper is to present some convergence properties of the iterative aggregation-disaggregation method for computing a stationary probability distribution vector of a column stochastic matrix. A sufficient condition for the local convergence property and the corresponding rate of convergence are established. Some global convergence considerations are presented. Several illustrati...

The analysis of flow in water-distribution networks with several pumps by the Content Model may be turned into a non-convex optimization uncertain problem with multiple solutions. Newton-based methods such as GGA are not able to capture a global optimum in these situations. On the other hand, evolutionary methods designed to use the population of individuals may find a global solution even for ...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...