Frans J. Peters

Parallel pivoting algorithms for sparse symmetric matrices

In this paper it is investigated which pivots may be processed simultaneously when solving a set of linear equations. It is shown that for dense sets of equations all the pivots must necessarily be processed one at a time; only if the set is sufficiently sparse, some pivots may be processed simultaneously. We present parallel pivoting algorithms for MIMD computers with sufficiently many processors and a common memory. Moreover we present algorithms for MIMD computers with an arbitrary, but fixed number of processors. For both types of computers algorithms embodying an ordering strategy are given.

Tree machines and divide-and-conquer algorithms

A tree machine consists of a number of processors (each with its own memory) mutually connected via communication branches so as to form a binary tree. Two processors may communicate only via a common communication link. Such a tree machine is a completely general, concurrent processing engine and can be used for problems decomposed in a hierarchical way. Implementation of divide-and-conquer algorithms on a tree machine is discussed. Algorithms for which a tree machine can be effective are characterized. Examples are shown and it is proven that for a class of k-dimensional divide-and-conquer algorithms the running time may be reduced from 0(N logk−1 N) on a sequential machine to 0(kN) on a tree machine.

An algorithm for transformations of pictures represented by quadtrees

Abstract Pictures that consist of discrete elements (pixels) are conveniently represented by quadtrees. This paper presents an algorithm to compute geometric transformations (translation, scaling, and rotation) of quadtrees.