A general asynchronous block iterative model with related convergence conditions

AbstractThis paper formulates a general time-varying asynchronous block-iterative model. A convergence condition for asynchronous block-iterations based on this model is given, compared to existing conditions for similar and shown to be strictly weaker

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Parallel Multisplittings For Optimization

. The philosophy of multisplitting methods is the replacement of a large-scale linear or nonlinear problem by a set of subproblems, each of which can be solved locally and independently in parallel by taking advantage of well-tested sequential algorithms. Because of this formulation most compute-intensive operations can be calculated independently and the algorithms are highly parallel. Recent developments for optimization, constrained and unconstrained, are described. These new algorithms are, in some cases, faster in sequential mode than conventional algorithms. Results of implementations on the Intel Paragon and on a cluster of workstations using PVM3 demonstrate superlinear speedup when compared with a standard test algorithm programmed in sequential mode. Further, the same algorithm when programmed in sequential mode also exhibits speedup when compared to the non-split algorithm. Key words. parallel algorithms, multisplitting, unconstrained optimization, QR decompositon, Househol..

Parallel Multisplittings for Constrained Optimization

. The philosophy of multisplitting methods is the replacement of a large-scale linear or nonlinear problem by a set of smaller subproblems, each of which can be solved locally and independently in parallel by taking advantage of well-tested sequential algorithms. Because of this formulation most compute-intensive operations can be calculated independently and the algorithms are highly parallel. In continuation of our earlier work we utilize a new parameter-free formulation of linearly constrained convex minimization problems to obtain a parallel algorithm of multisplitting type. Numerical results both serial and parallel are reported which demonstrate its efficiency and which also show that it compares favorably to our earlier parameter-dependent approach. Key words. Parallel algorithms, multisplitting, constrained optimization. Computing Reviews. D.1.3, G.1.6 1. Introduction We consider the general convex minimization problem minf(x) subject to h(x) = 0; g(x) 0: (1) Here, f : R n ..