. 
 
 UNIVERSITY OF 
 
 ILLINOIS UBRARY 
 
 ISI URSAlNA-CHAMPA'Cr-J 
 
 ENGINEERING 
 
NOTICE: Return or renew all Library Materials! The Minimum Fee for 
 each Lost Book is $50.00. jlj^ ^ 
 
 The person charging this material is'iw^nsible for 
 its return to the library from which it was withdrawn 
 on or before the Latest Date stamped below. 
 
 Theft, mutilation, and underlining of books are reasons for discipli- 
 nary aefiorkaftd may result in dismissal from pn University. 
 To renew fSlCTfJIephone Center, 333-8400 . 
 
 UNIVF^SlTY OF ILLINOIS LIBRARY 'AT ;,UfiBANA-CHAMPAIGN 
 
 L161— O-1096 
 
Digitized by the Internet Archive 
 
 in 2012 with funding from 
 
 University of Illinois Urbana-Champaign 
 
 http://archive.org/details/semiannualtechni74slot 
 
ENGINEERING LIBRAE 
 UNIVERSITY OF ILLINOIS 
 
 UR3ANA. ILLINOIS 
 
 ed Computation 
 
 UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN 
 
 URBANA. ILLINOIS 61801 
 
 1 
 
 CAC Document No. 7k 
 
 Center for Advanced Computation 
 SEMI-ANNUAL TECHNICAL REPORT 
 October 1, 1972 - March 31, 197 3 
 
CAC Document No. 'jh 
 
 SEMI-ANNUAL TECHNICAL REPORT OF 
 THE CENTER FOR ADVANCED COMPUTATION 
 October 1, 1972 - March 31, 1973 
 
 Center for Advanced Computation 
 University of Illinois at Urbana- Champaign 
 Urbana, Illinois 61801 
 
 Form Approved 
 Budget Bureau No. 22-R0293 
 
 The views and conclusions contained in this document are those of the 
 authors and should not be interpreted as necessarily representing the 
 official policies, either expressed or implied, of the Advanced Research 
 Projects Agency or the U. S. Government. This work was supported in 
 part by the Advanced Research Projects Agency of the Department of De- 
 fense and was monitored by the U. S. Army Research Office-Durham under 
 Contract No. DAHC04-72-C-0001: 
 
 Principal Investigator: D. L. Slotnick (217) 333-0925; 
 
 Contractor: Board of Trustees, University of Illinois; 
 
 Sponsored by: Advanced Research Projects Agency, ARPA Order No. 1899; 
 
 Program Code Number 2P10j Amount of Contract: $U, 000,6^6; 
 
 Dates: 12 July 1971 - 11 July 197^; 
 
 Title: ILLIAC IV Applications Research. 
 
 Approved for public release; distribution unlimited. 
 
IN6WEERMG LIBRARY 
 
 TABLE OF CONTENTS 
 
 Page 
 
 REPORT SUMMARY 1 
 
 1. APPLIED MATHEMATICS GROUP 2 
 
 1.1 Computational Methods in Linear Algebra 2 
 
 1.1.1 Solution of Systems of Linear Equations 2 
 
 1.1.2 The Algebraic Eigenvalue Problems 2 
 
 1.2 Linear Programming 3 
 
 1.3 Combinatorial Algorithms 3 
 
 l.k Approximation of Functions h 
 
 1.5 Integral Equations 5 
 
 1.6 ARPA Network 5 
 
 References 6 
 
 2. ILLIAC IV MULTISPECTRAL IMAGE PROCESSING 8 
 
 2.1 Image Processing for Pattern Recognition 8 
 
 3- ILLIAC IV LANGUAGE DEVELOPMENT FOR THE PHASE II SYSTEM .... 10 
 
 3.1 IDOL 10 
 
 k. ECONOMIC RESEARCH GROUP 11 
 
 k.l STEP I 11 
 
 k.2 STEP II 11 
 
 U.3 MEASURE 11 
 
 5- NETWORK SYSTEMS GROUP 12 
 
 5.1 Project to Interface the B67OO to the ARPA Network .... 12 
 
 5-2 ARPA Network Terminal System Development 12 
 
 5-3 ARPA Network Usage 13 
 
 5.U Further Installations of ANTS System on 
 
 the Network 13 
 
 5.5 Graphics Support for Center Projects 13 
 
 5.6 Hardware Acquisition .....' ik 
 
 5-7 Laboratory for Atmospheric Research Support Ik 
 
TABLE OF CONTENTS (continued) 
 
 Page 
 
 6. ADMINISTRATION 16 
 
 6.1 Fiscal Status 16 
 
 DOCUMENTS AND PUBLICATIONS 17 
 
 THESES 19 
 
1. 
 
 REPORT SUMMARY 
 
 This document reports progress on ARPA contract DAHC01+-72-C- 
 0001 entitled "ILLIAC IV Applications Research at the Center for 
 Advanced Computation, University of Illinois at Urbana-Champaign. " 
 The principal objective of this program is the development and testing 
 of numerical techniques and software systems for use of ILLIAC IV over 
 the ARPA Network. This is being accomplished through activities in 
 the following areas: 
 
 1. Development of numerical techniques suitable for parallel 
 processing in the areas of: 
 
 a) Computational methods and linear algebra 
 
 b) Linear programming 
 
 c) Combinatorial algorithms 
 
 d) Approximation of functions 
 
 e) Integral equations 
 
 f ) ARPA Network 
 
 2. Development of an ILLIAC IV multi spectral image processing 
 system 
 
 3- Development of ILLIAC IV language for the phase II system 
 k. Development of programs in large scale calculations such 
 as input-output economic modeling, quadratic assignment 
 algorithms for various classes of spatial allocation 
 problems, and atmospheric dynamics 
 5. Development of Network Access Computer System — ANTS 
 
2. 
 
 1. APPLIED MATHEMATICS GROUP 
 
 1.1 Computational Methods in Linear Algebra : 
 
 1.1.1 Solution of Systems of Linear Equations 
 
 Numerical methods for updating the solution x in Ax=f, due 
 to changes in rows, columns, or the disaggregation of a given row and 
 
 column into m rows and columns, have been developed [17 ] where the num- 
 
 2 ^ 
 
 ber of operations required are of order n instead of n J if the new 
 
 system were to be solved "from scratch. " These techniques increase 
 the computational efficiency of handling large input-output economical 
 models. Once the Leontief inverse is obtained for the original input- 
 output model, the above methods permit accurate determination of the 
 effects on the solution due to changes in the transaction data. 
 
 1.1.2 The Algebraic Eigenvalue Problem 
 
 In collaboration with members of the Chemistry Department, 
 a direct method for synthesis of magnetic resonance spectra has been 
 developed [6, 7]. Previously such spectra were computed by unwieldly 
 and inefficient iterative methods. The new method simply converts the 
 problem into one of solving a generalized eigenvalue problem. Since 
 the matrices involved are then of special form, some thought is being 
 given to improved methods of solving the generalized eigenvalue problem 
 which is obtained. 
 
 An efficient parallel algorithm for finding the leading 
 eigenvalues and eigenvectors of large sparse matrices is being developed. 
 
3- 
 
 This algorithm is a combination of Lanczos algorithm without reortho- 
 gonalization [l4] and the simultaneous iteration method [10 ]. 
 
 1.2 Linear Programming 
 
 The initial version of the Linear Programming algorithm for ILLIAC 
 IV has been completed and tested on the simulator. It is written in 
 Glypnir to enable rapid coding and will be tried on ILLIAC IV as soon 
 as the hardware is sufficiently reliable. A document [13] describing 
 the algorithm, a numerically stable version of the simplex method based 
 on work by Gill and Murray [9] and Saunders [18], has been produced. 
 Further enhancements to improve the speed of the algorithm are in hand, 
 also theoretical work to adapt the algorithm to handle larger problems 
 requiring auxiliary storage has been done. 
 
 A matrix generator language has been developed to allow 
 rapid specification of large matrices, mainly for use in large linear 
 programming problems. This provides the user with the capability to 
 create a matrix made up of many submatrices of specific types corre- 
 sponding to some economic or physical model. Implementation of this 
 algorithm is proceeding, and it is hoped that eventually it will be 
 used to generate a code for ILLIAC IV in such a way as to allow storage 
 of large matrices very economically. To this end some code has been 
 written for ILLIAC IV to handle special types of substructures (e.g. 
 diagonal matrices, lower triangular matrices.) However, much work re- 
 mains to be done. 
 
 1. 3 Combinatorial Algorithms 
 
 The DuLmage-Mendolsohn algorithm [8] for finding maximum 
 
k. 
 
 matchings in bipartite graphs was programmed, in PL/ 1 and tested as part 
 of the work on optimal lower triangularization of sparse matrices. 
 
 A theoretical report on the quadratic assignment problem was 
 finished and published as a CAC document [l6]. 
 
 A technical memorandum [15 ] was published on the new, parallel 
 algorithm for clique detection. The PL/ 1 program is now clearly 
 commented. 
 
 A completely new algortihm for clique detection has been 
 developed, written and tested in PL/ I; given the cliques of a graph G, 
 which is a subgraph of Graph G' with the same nodes, but fewer edges, 
 this new algorithm finds the cliques of G' from those of G. In graphs 
 arising from a threshold applied to a symmetric matrix, an algorithm 
 of this type enables the threshold to vary dynamically. 
 l.k Approximation of Functions 
 
 A study of simultaneous uniform approximation of sets of curves 
 by straight lines with different intercepts but common slope was com- 
 pleted [2, 3l« The more difficult (but related) problem of imple- 
 menting and testing an algorithm for simultaneous approximation by 
 exponentials with common exponential factor was then tackled. Two 
 distinct computer programs were ultimately written. In one improved 
 approximations were constructed using the solutions of certain linear 
 inequalities. The other program uses Remez-type techniques (successive 
 approximations of error maxima) . This second method was by far the 
 fastest, but experience with the first method has been valuable in that 
 it should be more easily extended to situations involving more compli- 
 
5- 
 
 cated approximating functions, such as sums of exponentials. More 
 information on this work will be available in [h], a condensed version 
 of which has been prepared for publication [5]. 
 
 In another line of work, application of a previously developed 
 theory [12] to approximation by families with a fixed point has been 
 worked out [11]. Such approximation should be very useful in certain 
 practical situations, for example in fitting an experimental curve by a 
 theoretical one which according to theory must pass through a given 
 point (the origin, for instance) . 
 
 1.5 Integral Equations 
 
 A brief survey of methods available for the numerical solution 
 of integral equations showed that an area particularly in need of study 
 is that of methods for solving integrodifferential equations of the type 
 arising in population dynamics or in other physical situations governed 
 by dynamic equations which include the past history of the system (e.g. 
 fatigue effects) . Some computer experiments were done and a theoretical 
 stability analysis was carried out for a simple first order method [l]. 
 
 1.6 ARPA Network 
 
 A security code was developed for the ARPA Network. The 
 code enables a user to log onto the system by using his code number Xi 
 which is immediately transformed into a pseudo code word Yj_ = f(X-j_) by 
 the host computer. Even though Yj_ and f are public knowledge it is not 
 possible to gain access to the system without knowing X, and the 
 equation Y = f(x) cannot be solved for X, even if Y is known. 
 
6. 
 
 REFERENCES 
 
 1. G. G. Belford, "Absolute Stability of Euler's Method for Integro- 
 
 Differential Equations, " Submitted to Numer . Math . 
 
 2. G. G. Belford, "An Algorithm for Fitting Related Sets of Straight- 
 
 line Data," CAC Document No. 5h, University of Illinois at 
 Urbana-Champai gn, 1972 • 
 
 3. G. G. Belford, "Fitting Related Sets of Straight-line Data, " Journal 
 
 of Cybernetics , to appear. 
 
 k. G. G. Belford, "Simultaneous Fitting of Exponential Decay Curves," 
 CAC Document No. 6l, University of Illinois at Urbana- 
 Champaign, April 1973 • 
 
 5« G. G. Belford, "Vector-Valued Approximation and Its Application to 
 Fitting Exponential Decay Curves," Math . Comp . , to appear. 
 
 6. R. L. Belford, G. G. Belford, "Eigenfield Expansion Technique for 
 
 Efficient Computation of Field-Swept Fixed-Frequency Spectra 
 from Relaxation Master Equations, " Journal of Chemical Physics, 
 to appear. 
 
 7. R. L. Belford, G. G. Belford and J. F. Burkhalter, "Eigenfields: A 
 
 Practical Direct Calculation of Resonance Fields and Inten- 
 sities for Field-Swept Fixed-Frequency Spectrometers, " 
 Journal of Magnetic Resonance, to appear. 
 
 8. A. L. Dulmage and N. S. Mendolsohn, "Two Algorithms for Bipartite Graphs, 
 
 Journal of SIAM Applied Mathematics , Vol. 11, pp. 183-19^, 
 196T 
 
 9. P. E. Gill and W. Murry, "A Numerically Stable Form of the Simplex 
 Algorithm, " Technical Report No Mathematics , Vol. 87; 
 National Physical Laboratory, Teddington, 1970- 
 
 10. A. Jennings, "A Direct Iteration Method of Obtaining Latent Roots and 
 
 Vectors of a Symmetric Matrix, " Proceedings of the Cambridge 
 Philosophical Society , Vol. 63, pp\ 755-765, 1967. 
 
 11. E. H. Kaufman and G. G. Belford, "Approximation by Families of 
 
 Functions with a Fixed Point, " in preparation. 
 
 
7- 
 
 12. E. H. Kaufman Jr. and G. G. Belford, "A Generalization of the 
 
 Vari solvency and Uni solvency Properties, " Journal of Approxi - 
 mation Theory , Vol. 7, pp. 21-35, 1973- 
 
 13. J. Lermit, "A Linear Programming Implementation, " CAC Document No. 
 
 k6, University of Illinois at Urbana-Champaign, October 1972. 
 
 Ik. C. C. Paige, "Computational Variants of the Lanczos Method for the 
 Eigenproblem, " Journal of Inst. Maths. Applies. , Vol. 10, 
 PP. 373-381, 1972. 
 
 15. G. Purdy, "Finding the Cliques of a Graph," CAC Technical Memorandum 
 
 No. 5. 
 
 16. G. Purdy, "The Quadratic Assignment Problem," CAC Document No. 71, 
 
 University of Illinois at Urbana-Champaign, April 1973- 
 
 17. A. Sameh and R. Bezdek, "Methods for Increasing the Computational 
 
 Efficiency of Input-Output and Related Large Scale Matrix 
 Operations, " CAC Document No. 66, University of Illinois at 
 Urbana-Champaign, 1973- 
 
 18. A. M. Saunders, "Large-Scale Linear Programming Using the Choleghy 
 
 Factorization, " Computer Science Department, Stanford Univer- 
 sity, STA-CS-72-252, January 1972. 
 
8; 
 
 2. ILLIAC IV MULTISPECTRAL IMAGE PROCESSING 
 
 2.1 Image Processing for Pattern Recognition 
 
 In March the Center successfully completed grant negotiations 
 with NASA/ AMES in support of system developments for ILLIAC IV inter- 
 pretation of ERTS-1 imagery. CAC has completed ILLIAC codes for 
 nonsupervised clustering of resolution elements into those terrain 
 categories most separable with respect to spectral properties, and 
 multivariate Gaussian statistical classification of image points into 
 aggregate terrain categories. This work has been conducted with partic- 
 ipation by the Laboratory for the Applications of Remote Sensing 
 (LARS) of Purdue University. Progress in now underway to verify the 
 correctness of these parallel codes by comparison with output from the 
 LARS serial computing system. Reports on this work should be completed 
 for NASA and ARPA by midsummer. 
 
 It is expected that the scope of this project will be ex- 
 tended in the next few months with additional support from the EROS 
 program of USGS/DI to include the design of a more comprehensive ILLIAC- 
 ERTS image processing system to support NASA/USGS earth resource moni- 
 toring objectives. 
 
 In addition to present contractural commitments, CAC is 
 investigating a new methodology for general image processing and pattern 
 recognition work which is expected to contribute to the solution of 
 
9. 
 
 image registration problems occurring within the analysis of resource 
 "boundary changes over time. The method employed also seems applicable 
 to a wider class of pattern recognition problems where prototype-derived 
 patterns are to be classified. A report on this work to NASA and ARPA 
 is forthcoming. 
 
10. 
 
 3. ILLIAC IV LANGUAGE DEVELOPMENT FOR THE PHASE II SYSTEM 
 
 3-1 IDOL 
 
 Although the IDOL report was not an overwhelming success (from 
 the point of view that it elicited no support for implementation), the 
 work performed to define IDOL revealed that there is something to be 
 gained "by applying the storage management techniques which form the 
 foundation for the IDOL approach in contexts other than that of ILLIAC IV. 
 A language and compiler which could provide accurate working set infor- 
 mation to an operating system prepared to use it could (on the basis of 
 Belady's work) permit a 100 per cent increase in throughput in the same 
 physical memory. Generalization of the techniques suggested could be used 
 to intelligently control the flow of information between levels of a 
 memory hierarchy ( of more than two levels). 
 
11, 
 
 k. ECONOMIC RESEARCH GROUP 
 k.l STEP I 
 
 During this period, work under ARPA support °f STEP I was 
 completed. The STEP I system has been used for several forecasts of 
 occupational employment for the United States and is to be maintained 
 and applied as need arises. 
 
 The principal research activity of the group under ARPA support 
 has emphasized the development of efficient computational algorithms for 
 large linear computations in which matrices are subject to modifications 
 of one or a few rows or columns. 
 k.2 STEP II 
 
 Members of the group responsible for STEP II have left employment 
 at the Center for other positions. As a result, planning and design of 
 STEP II under ARPA support has been temporarily suspended. 
 k.3 MEASURE 
 
 Work on the MEASURE activity has been transferred to the 
 Information System Group. 
 
12, 
 
 5- NETWORK SYSTEMS GROUP 
 
 5.1 Project to Interface the B67OO to the ARPA Network 
 
 Daring the period, the University of California at San Diego 
 (UCSD) 67OO entry to the network was improved and expanded. The Center 
 will no longer have any responsibility in the area of interfacing Burroughs 
 B6700's to the network. 
 
 5.2 ARPA Network Terminal System Development 
 
 During the reporting period, development of ANTS progressed in 
 completing the Mark I system, and initial design and coding efforts on the 
 Mark II system progressed. 
 
 The Mark I system is now stabilized and a crash rate of 1 to 3 
 per day has been attained. No further activities will be involved in up- 
 grading or maintaining Mark I as all Center personnel will be involved in 
 the development of the Mark II system. 
 
 The remaining efforts of the group during the period were to 
 complete software necessary to operate with the UCSD computer center via 
 the network , to upgrade the PEESPOL compiler for additional support in 
 developing Mark II ANTS for the next reporting period and to lay down the 
 design specifications for the Mark II system. 
 
 The Mark II system design is complete to the point of allowing 
 initial coding and debugging activities to begin. It is expected that 
 during the second quarter of 1973> the Mark II system will be brought to 
 an operational status, first to a level equivalent to the Mark I system 
 
13. 
 
 and then later to include increasing numbers of peripheral devices, proto- 
 cols and associated activities. 
 5-3 ARPA Network Usage 
 
 During the reporting period, network usage continued very hea- 
 vily on the UCSD B67OO system, UCLA 360/91 (both for RFE and TSO usage), 
 various Tenex systems around the network (predominantly USC-ISl), the 
 Multics system, and the Ames TSS 360/67 system. Initial efforts were 
 begun during the reporting period to begin access and experimental usage 
 of the ILLIAC IV complex at Ames. 
 5.U Further Installation of ANTS Systems on the Network 
 
 During the reporting period, more contacts were made with addi- 
 tional sites for information as to the availability of an ANTS system to 
 provide those sites with access to the network. The University of 
 California at Los Angeles has elected to replace their Sigma 7 computer 
 system with an ANTS for access to the network in the network measurement 
 project supported by ARPA. Additionally, further work is in progress 
 with the Army to establish possible follow-up on activities in the install- 
 ation of additional sites. 
 5. 5 Graphics Support for Center Projects 
 
 With the advent of the UCSD 67OO system as a service site on 
 the network, graphics activities were continued and the development of a 
 full blown user-oriented graphics package initiated. Fancy ARPA Network 
 Graphics System ( FANGS) will provide a very sophisticated and highly in- 
 teractive system for doing graphical analysis and display of user desired 
 
11+ . 
 
 imagery. Additionally, programs were developed for bringing back 
 graphical images to various CAC equipment such as the Gould plotter, 
 Computek graphics copies, the IMLAC Display, and a soon to be acquired 
 drum plotter system. 
 
 Additional work is being initiated in the production of half 
 tone imagery on the IMLAC Display as a supporting function to the ERTS 
 imagery project which will be developing algorithms and analysis system 
 on ILLIAC IV for ERTS imagery. 
 5-6 Hardware Acquisition 
 
 During the reporting period, negotiations were completed with 
 the Digital Equipment Corporation for additional hardware at the Center 
 based on the advanced concepts PDP-11 model 1+5 processor and memory sys- 
 tem to provide Center research personnel with an advanced capability 
 access system for the ARPA Network. The software system, known as The 
 Network Imbedded Computer Executive (NICE) will be developed for the 
 11-1+5 • Design activities will begin during the next reporting period. 
 5-7 Laboratory for Atmospheric Research Support 
 
 Support for the University of Illinois at Urbana-Champaign's 
 Laboratory for Atmospheric Research (LAR), under the direction of 
 Professor Ogura, consisted of the procurement of a drum plotting device, 
 to be attached to the Center's ANTS system, and the writing of graphics 
 packages at several network sites for display of the laboratory's 
 research results. 
 
 The drum plotter was ordered during the reporting period and 
 will be delivered in May, 1973- 
 
15. 
 
 Basic graphics display software was written on the UCLA 
 360/91 and the University of Southern California's Information 
 Services Institute's PDP-10 for display of the laboratory's meteor- 
 ology research results. Graphics images can be returned from either 
 place to the IMLAC display, the Computek storage scope or the GOULD 
 printer/plotter attached to ANTS 
 
 During the next reporting period, inhouse graphics display 
 software will be written at UCLA and USC-ISI to provide more soph- 
 isticated output of LAR results. The plotter will be interfaced to 
 ANTS and added to the repertoire of graphics devices available to 
 LAR researchers. 
 
16. 
 
 ADMINISTRATION 
 
 6.1 Fiscal Status 
 
 Actual expenditures through 30 September 1972: $1,527,323. 
 Estimated expenditures and obligations for the six month period 
 covered in this report ( 1 October 1972 - 31 March 1973): 
 
 October 106,73*+ 
 
 November 132,550 
 
 December 108,972 
 
 January 12k, 933 
 
 February 86, k 52 
 
 March l4l, 058 
 
 700, 699 
 Total expenditures and obligations through 31 March 1973: $2,228,022. 
 
IT. 
 
 DOCUMENTS AND PUBLICATIONS 
 
 G. G. Belford, "An Algorithm for Fitting Related Sets of Straight- 
 Line Data, " CAC Document No. ^k, University of Illinois at 
 Urbana-Champaign, December 13, 1972. 
 
 G. G. Belford, "A Generalization of the Vari solvency and Uni solvency 
 Properties," Journal of Approximation Theory , 'J'.l (1973)? 
 with E. H. Kaufman, Jr. 
 
 G. G. Belford, "Simultaneous Fitting of Exponential Decay Curves, " 
 CAC Document No. 6l, University of Illinois at Urbana- 
 Champaign, April 1, 1973- 
 
 G. G. Belford, R. J. Lermit, G. B. Purdy, and A. H. Sameh, "Computa- 
 tional Mathematics Abstracts, " CAC Document No. 6k, 
 University of Illinois at Urbana-Champaign, February, 1973- 
 
 J. T. Chen, "Quadratic Programming for Least-Cost Feed Formulation 
 Under Probabilistic Protein Constraint, " American Journal 
 of Agricultural Economics , May 1973- 
 
 J. T. Chen, "Separable Programming for Considering Risk in Farm Plan- 
 ning: Comment, " American Journal of Agricultural Economics , 
 February 1973- 
 
 P. T. Cichy, "The Use of ILLIAC IV to Solve Numerical Fluid Dynamics 
 Problems, " CAC Document No. 67? University of Illinois at 
 Urbana-Champaign, March 1973- 
 
 J. H. Ericksen, "Iterative and Direct Methods for Solving Poisson's 
 
 Equation and Their Adaptability to ILLIAC IV, " CAC Document 
 No. 60, University of Illinois at Urbana-Champaign, March 
 1973. 
 
 R. J. Lermit, "Numerical Methods for the Identification of Differen- 
 tial Equations," CAC Document No. k9, University of Illinois 
 at Urbana-Champaign, June 12, 1972- 
 
 R. J. Lermit and J. M. Randal, "Augmented Significance Routines for 
 ILLIAC IV," CAC Document No. 56, University of Illinois at 
 Urbana-Champaign, December 1972. 
 
 M. Ogura, M. S. Sher and J. H. Ericksen, "A Study of the Efficiency 
 of ILLIAC IV in Hydrodynamic Calcualtions, " CAC Document 
 No. 59? University of Illinois at Urbana-Champaign, December 
 11, 1972. 
 
18. 
 
 G. B. Purdy, "Some Extremal Problems in Geometry and Analysis, " CAC 
 Document No. 52, University of Illinois at Urbana-Champaign, 
 July 1, 1972. 
 
 G. B. Purdy, "The Quadratic Assignment Problem, " CAC Document No. 71, 
 University of Illinois at Urb ana- Champaign, February 1973 • 
 
 S. Rajan, "A Computational Technique for High Subsonic Compressible 
 Flow Past a Circular Cylinder on a Parallel Computer, " CAC 
 Document No. 50, University of Illinois at Urbana-Champaign, 
 October 20, 1972. 
 
 S. Raj an, "Evaluation of Numerical Viscosity Effects in Transonic 
 Flow Calculations, " CAC Document No. 62, University of 
 Illinois at Urbana-Champaign, January 1973- 
 
 R. M. Ray III, "A Generalized ILLIAC IV Urban Land Use Planning Model," 
 CAC Document No. 51* University of Illinois at Urbana- 
 Champaign, October 1972. 
 
 A. L. Redwood, "Population Projections for Manpower Planning, " CAC 
 Document No. 55 > University of Illinois at Urbana-Champaign, 
 February 15, 1973- 
 
 A. H. Sameh, "On Jacobi and Jacobi-Like Algorithms for a Parallel 
 
 Computer, " CAC Document No. 57> University of Illinois at 
 Urbana-Champaign, December 11, 1972. 
 
 A. H. Sameh and R. H. Bezdek, "Methods for Increasing the Computational 
 Efficiency of Input-Output and Related Large Scale Matrix 
 Operations, " CAC Document No. 66, University of Illinois at 
 Urbana-Champaign, February 1973* 
 
 A. H. Sameh and W. L. Heimerdinger, "On the Identification of Multi- 
 Output Linear Time-Invariant and Periodic Dynamic Systems, " 
 CAC Document No. 53* University of Illinois at Urbana-Champaign, 
 November 1, 1972. 
 
 S. A. Schuster, "Locating Optimal Sites in Geographic Information 
 Systems," CAC Document No. 72, University of Illinois at 
 Urbana-Champaign, June 9, 1973- 
 
 J. E. Stevens, Jr., "Fast Heuristic Techniques for Placing and Wiring 
 Printed Circuit Boards, " CAC Document No. 58, University of 
 Illinois at Urbana-Champaign, October 1972- 
 
19- 
 
 THESES 
 
 S. A. Schuster, "Locating Optimal Sites in Geographic Information 
 
 Systems," Ph.D. Thesis directed by D. L. Slotnick, June 9, 
 1973- 
 
 J. E. Stevens, Jr., "Fast Heuristic Techniques for Placing and Wiring 
 Printed Circuit Boards," Ph.D. Thesis directed by D. L. 
 Slotnick, October 1972. 
 
 
UNCLASSIFIED 
 
 Security Classification 
 
 DOCUMENT CONTROL DATA -R&D 
 
 (Security cleaalllcetlon ol title, body of aba tract and Indearng annotation imiK be entered when the overall report la claeellled) 
 
 ORIGINATING ACTIVITY (Corporal* author) 
 
 Center for Advanced Computation 
 University of Illinois at Urb ana- Champaign 
 Urbana, Illinois 6l801 
 
 la. REPORT SECURITY CLASSIFICATION 
 
 UNCLASSIFIED 
 
 2b. GROUP 
 
 REPORT TITLE 
 
 Semi-Annual Technical Report of the Center for Advanced Computation, 
 October 1, 1972 - March 31, I973 
 
 DESCRIPTIVE NOTE* (Type ot report and htclualvm datea) 
 
 Technical report 
 
 autmor(S) (Flrat nmmra, middle Initial, laet name) 
 
 Center for Advanced Computation 
 
 REPORT DATE 
 
 May 1, 1973 
 
 7a. TOTAL NO. OF PACES 
 
 21 
 
 76. NO. OF REFS 
 
 18 
 
 I. CONTRACT OR GRANT NO. 
 
 DAHC04-72-C-0001 
 
 I PROJECT NO. 
 
 AREA Order No. 1899 
 
 we. ORIGINATOR'S REPORT NUMBER(S) 
 
 CAC Document No. 7^ 
 
 9b. OTHER REPORT NOISI (Any other number* that may be aaalaned 
 thla report) 
 
 }. DISTRIBUTION STATEMENT 
 
 Copies may be requested from the address given in (l) above, 
 
 ■ SUPPLEMENTARY NOTES 
 
 None 
 
 12. SPONSORING MILITARY ACTIVITY 
 
 U. S. Army Research Office-Durham 
 
 Duke Station 
 
 Durham, North Carolina 
 
 I. ABSTRACT 
 
 See the Report Summary on page 1 within the report itself. 
 
 )D '•'T..1473 
 
 UNCLASSIFIED 
 
 Security Classification 
 
UNCLASSIFIED 
 
 Security Classification 
 
 KEY WORDS 
 
 Applied Mathematics Group 
 
 ILLIAC IV Multispectral Image Processing 
 
 ILLIAC IV Language Development for the 
 Phase II System 
 
 Economic Research Group 
 
 Network Systems Group 
 
 Administration 
 
 UNCLASSIFIED 
 
 Security Classification