Table Of ContentNAVAL POSTGRADUATE SCHOOL
Monterey, California
THESIS
HYPERCUBE SOLUTIONS
FOR
CONJUGATE DIRECTIONS
by
Jonathan Edward Hartman
December, 1991
Thesis Co-Advisor: William B. Gragg
Thesis Co-Advisor: Uno R. Kodres
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I NAME OF PERFORMING ORGANIZATION 6b OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION
Computer Science Department (ifapplicable)
Naval Postgraduate School cs Naval Postgraduate School
I ADDRESS (City, State, and ZIP Code) 7b ADDRESS (City, State, and ZIP Code)
Monterey, CA 93943 Monterey, CA 93943
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PROGRAM PROJECT TASK WORK UNIT
ELEMENT NO. NO. NO. ACCESSION NO.
TITLE (Include Security Classification)
HYPERCUBE SOLUTIONS FOR CONJUGATE DIRECTIONS
PERSONAL AUTHOR(S)
Hartman. Jonathan Edward
TYPE OF REPORT 13b TIME COVERED 14 DATE OF REPORT (Year, Month, Day) 15. PAGE COUNT
Master's Thesis FROM 06/89 TO 12/91 December 1991 380
SUPPLEMENTARY NOTATION
The views expressed in this thesis are those of the author and do not reflect the
iTicial policy or position of the Department of Defense or the United States Government.
COSATI CODES 18. SUBJECT TERMS (Continue on reverse ifnecessary and identify by block number)
Conjugate Gradients, Gaussian Elimination, Gauss Factorization, Hyper-
FIELD GROUP SUB-GROUP
cube, iPSC/2, Matrices, Multiprocessors, Transputers, Communicating
Sequential Processes, Message Passing, Distributed Memory, MIMD.
I ABSTRACT (Continue on reverse ifnecessary and identify by block number)
As computing machines advance, new fields are explored and old ones are expanded. This thesis considers
irallel solutions to several well-known problems from numerical linear algebra, including Gauss Factorization
id the method of Conjugate Gradients. The Gauss algorithm was implemented on two parallel machines: an
— —
itel iPSC/2, and a network of INMOS T-800 transputers. Interprocessor communication in both cases was
orne by a hypercube interconnection topology.
The results reveal general findings from parallel computing and more specific data and information con-
;rning the systems and algorithms that were employed. Communication is timed and the results are analyzed,
lowing typical features of a message passing system. System performance is illustrated by results from the
auss codes. The use of two different pivoting strategies shows the potential and the limitations of a parallel
iachine. The iPSC/2 and transputer systems both show excellent parallel performance when solving large,
snse, unstructured systems. Differences, advantages, and disadvantages of these two systems are examined and
cpectations for current and future machines are discussed.
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>a. NAME OF RESPONSIBLE INDIVIDUAL 22b. TELEPHONE (Include Area Code) 22c. OFFICE SYMBOL
Uno R. Kodres (408) 646-2197 CSKr
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Approved for public release; distribution is unlimited.
HYPERCUBE SOLUTIONS
for
CONJUGATE DIRECTIONS
by
Jonathan Edward Hartman
Captain. United States Marine Corps
B.S.. United States Naval Academy, 1984
Submitted in partial fulfillment of the
requirements for the degrees of
MASTER OF SCIENCE IN COMPUTER SCIENCE
MASTER OF SCIENCE IN APPLIED MATHEMATICS
from tIk-
naval POSTGRADUATE SCHOOL
December, 1991
ABSTRACT
As computing machines advance, new fields are explored and old ones are ex-
panded. This thesis considers parallel solutions to several well-known problems
from numerical linear algebra, including Gauss Factorization and the method of
Conjugate Gradients. The Gauss algorithm was implemented on two parallel ma-
chines: an Intel iPSC/2, and a network of INMOS T-800 transputers. Interprocessor
— —
communication in both cases was borne by a hypercube interconnection topology.
The results reveal general findings from parallel computing and more specific
data and information concerning the systems and algorithms that were employed.
Communication is timed and the results are analyzed, showing typical features of
a message passing system. System performance is illustrated by results from the
Gauss codes. The use of two different pivoting strategies shows the potential and
the limitations of a parallel machine. The iPSC/2 and transputer systems both
show excellent parallel performance when solving large, dense, unstructured systems.
Differences, advantages, and disadvantages of these two systems are examined and
expectations for current and future machines are discussed.
111
tttftt.
d.l
THESIS DISCLAIMER
The computer programs developed in this research have not been exercised for
all cases of interest. Every reasonable effort has been made to eliminate computa-
tional and logical errors, but the programs should not be considered fully verified.
Any application of these programs without additional verification is at the user's
risk. A reasonable effort has been put forth to make the code efficient. Optimization
has been suppressed, however, in areas where it would jeopardize the simplicity and
clarity of the algorithm without great reward in terms of performance.
IMS, inmos, and occam are trademarks of INMOS Limited, a member of the
SGS-THOMSON Microelectronics Group. INTEL, intel, and iPSC are trademarks
of Intel Corporation. IBM, PC AT, and PC XT are registered trademarks of Inter-
national Business Machines Corporation. CIO, LD-ONE, LD-NET, TASM, TCX,
TIO, TLIB, and TLNK are trademarks of Logical Systems. MS-DOS is a trademark
of Microsoft Corporation. MATLAB is a trademark of The MathWorks, Inc. All
other brand and product names are trademarks or registered trademarks of their
respective companies.
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