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Every solution is either trivial or false.
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| -- Zhijing George Mou. |
Ordered by date of original research or of publication.
C. F. Gauss, "Nachlass, Theoria Interpolationis Methodo Nova
Tractata," in Carl Friedrich Gauss Werke, Band 3, Koniglichen
Gesellschaft der Wissenschaften: Gottingen, pp. 265-330, 1866.
H. BURKHARDT,"Trigonometrische Interpolation," in Chapter 9, Encyklopiidie der
Mathematischen Wissenschaften, vol. 2, part 1, 1st half, 1899-1916.
H. BURKHARDT,"Trigonometrische Reihenund Integrale(bis etwa
1850)," in Chapter 12, Encyklopiidie der Mathematischen
Wissenschaften,vol. 2, part 1, 2nd half, 1904-1916.
J. W. COOLEY & J. W. TUKEY, "An Algorithm for the Machine
Calculation of Complex Fourier Series," Math. Comput., Vol. 19,
no. 2, pp. 297-301, Reprinted in Digital
Signal Processing, ed. Larry R. RABINER & C. M. RADER, pp. 223-227, New
York: IEEE Press, 1972, Apr. 1965.
Alan Perlis, The Synthesis of Algorithmic Systems, The 1st Turing
Lecture. (ACM V 14 No 1, 1967).(cached copy here)
Donald Fraser. Array permutation by index-digit
permutation. Journal of ACM, 23(2):298—309, April 1976.
The 1977
Turing Lecture. Can Programming Be Liberated from the von
Neumann Style? A Functional Style and Its Algebra of Programs, by
John Backus, IBM Research Laboratory, San Jose CA
MICHAEL T. HEIDEMAN, DON H. JOHNSON, C. SIDNEY BURRUS "Gauss and
the History of the Fast Fourier Transform", 1985. Rice U
Eng. Dept.
cached copy here.
Z. G. Mou and P. Hudak. An algebraic model for divide-and-conquer
algorithms and its parallelism. The Journal of Supercomputiug,
2(3):257-278, November 1988.
cached copy here.
The design and analysis of parallel algorithms / by Selim G. Akl.
1989, Prentice Hall textbook,
cached copy here.
This was the state of the art before George Mou.
Zhijing George Mou, A Formal Model for Divide-and-Conquer and Its
Parallel Realization, May 1990, Research Report
YALEU/DCS/RR-795. (Yale
PhD Thesis)
Z. G. Mou. Divacon: A parallel language for scientific computing
based on divide-and-conquer. In Proceedings of the Third
Symposium on the Frontiers of Massively Parallel Computation,
pages 451-461. IFEE, October 1990.
Z. G. Mou and M. Goodman, "A Comparison of Communication Costs
for Three Parallel Programming Paradigms on Hypercube and Mesh
Architectures". Proc. 5th SIAM Conf. on Parallel Processing
p491-500, held in Houston TX March 1991.
ACM
link here.
Z. G. Mou, C. Constantinescu, and T. Hickey. Divide-and-conquer
on a 3-dimensional mesh. In Proceedings of the European Workshops
on Parallel Computing, pages 344-355, Barcelona, Spain, March
1992.
Z.G.Mou, Cornel Constantinescu, and T. Hickey. Optimal mappings
of divide-and-conquer algorithms to mesh connected parallel
architectures. In Proceedings of International Computer
Symposium, pages 273-284, Taiwan, December 1992.
Z. George Mou and Xiaojing Wang, Optimal Mappings of m
Dimensional FFT Communication to k Dimensional Mesh for Arbitrary
m and k. pp 104-119. in PARLE '93, Parallel Architectures and
Languages Europe, Lecture Notes in Computer Science #694,
Springer-Verlag. 5th International PARLE Conference, Munich,
Germany, June 1993 Proceedings.
cached copy here.
Jeffrey Yepez, Guy P. Seeley, and George Mou. Lattice-gas
automata on parallel architectures. In Proceedings of
International Symposium on Parallel Computation, pages 522–525,
1993. Beijing, China. (For review on lattice gas automata see
The Classical Lattice-Gas Method by Jeffrey Yepez 1999,
DTIC/ADA455835.pdf).
Google's
MapReduce paper MapReduce: Simplified Data Processing on
Large Clusters Jeffrey Dean and Sanjay Ghemawat, 2004.
Zhijing G. Mou, Hai Liu, Paul Hudak, Compress-and-Conquer for
Optimal Multicore Computing, In Proceedings of the POPL 2010
Workshop on Declarative Aspects of Multicore Programming, DAMP
2010, Madrid, Spain, January 19, 2010.
ACM link here,
ResearchGate link here,
cached copy here.
Z. George Mou, Black-White Array: A New Data Structure for
Dynamic Data Sets. April 2020, arXiv preprint here. cached
copy here.
Orian Leitersdorf, Yahav Boneh, Gonen Gazit, Ronny Ronen, Shahar
Kvatinsky, FourierPIM: High-Throughput In-Memory Fast Fourier
Transform and Polynomial Multiplication Viterbi Faculty of
Electrical and Computer Engineering, Technion – Israel Institute
of Technology, Haifa, 3200003, Israel. ArXiv 2304.02336v1
[cs.AR] 5 Apr 2023.
Patent US20230351547A1, Methods and control systems that use
dimensional-transform-based three-dimensional searching and voxel
mapping. Published 02-November-2023.
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