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Abstract
The main goal of this project is to investigate, develop, and implement algorithms for numerical linear algebra on parallel computers in order to acquire expertise in methods for parallel computations. An important motivation for analyzaing and investigating the potential for parallelism in these algorithms is that many scientific applications rely heavily on the performance of the involved dense linear algebra building blocks. Even though we consider the distributedmemory as well as the sharedmemory programming paradigm, the major part of the thesis is dedicated to distributedmemory architectures. We emphasize distributedmemory massively parallel computers  such as the Connection Machines model CM200 and model CM5/CM5E  available to us at UNIC and at Thinking Machines Corporation. The CM200 was at the time this project started one of the few existing massively parallel computers. Several areas in the numerical linear algebra field are investigated and they illustrate the problems that arise as well as the techniques that are related to the use of massively parallel computers: 1.Study of Strassen's matrixmatrix multiplication on the Connection Machine model CM200. What performance can we expect to achieve? Why? 2.Solving systems of linear equations using a Strassentype matrixinversion algorithm. A good way to solve systems of linear equations on massively parallel computers? 3.Aspects of computing the singular value decomposition on the Connection Machine CM5/CM5E. What are the quidelines to follow in order to achieve an efficient, highly parallel and scalable implementation of the considered algorithms? What are the numerical properties of our implementation? 4.A relatively new algorithm to compute the singular vectors of bidiagonal matrix via Rutishauser's qd algorithm is investigated. this algorithm is built on top of several scanoperations. What difficulties occur when implementing this algorithm to massively parallel computers?
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  101 
Publication status  Published  1995 
Series  IMMPHD199515 

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Dive into the research topics of 'Distributedmemory matrix computations'. Together they form a unique fingerprint.Projects
 1 Finished

Numerisk lineær algebra på massivt parallele datamater
Balle, S. M. & Nielsen, H. B.
01/06/1992 → 02/08/1995
Project: PhD