Mathematical applications, computation, and complexity
Author:
Hirsh Cohen
Journal:
Quart. Appl. Math. 30 (1972), 109-121
DOI:
https://doi.org/10.1090/qam/99736
MathSciNet review:
QAM99736
Full-text PDF Free Access
References |
Additional Information
- Theodore von Kármán, The engineer grapples with non-linear problems, Bull. Amer. Math. Soc. 46 (1940), 615–683. MR 3131, DOI https://doi.org/10.1090/S0002-9904-1940-07266-0
T. von Karman, Tooling up mathematics for engineering, Quart. Appl. Math. 1, 1 (1943)
- The mathematical sciences: A collection of essays, The M.I.T. Press, Cambridge, Mass.-London, 1969. Edited by the National Research Council’s Committee on Support of Research in the Mathematical Sciences (COSRIMS) with the collaboration of George A. W. Boehm. MR 0235955
A. Weyl, Appendix to C. B. Lévi-Strauss, Les structures élémentaires de la parenté, Presses universitaires de France, Paris, 1949
N. Chomsky, Formal properties of grammars, in Handbook of Math. Psych., ed. R. D. Luce, R. R. Bush, and E. Galanter, John Wiley, New York 1963, Vol. 2
D. C. Gazis, A computer model for the financial analysis of urban housing projects, Socio-Econ. Plan. Science 5, 125–144 (1971)
- Hirsh Cohen, Nonlinear diffusion problems, Studies in applied mathematics, Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N. J.), 1971, pp. 27–64. MAA Studies in Math., Vol. 7. MR 0447846
R. FitzHugh, Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber, Biophys. J. 2, 11–21 (1962)
W. L. Hardy, Propagation speed in myelinated nerve: dependence on external sodium, Ph.D. dissertation, University of Washington (1969)
R. Stein, The role of spike trains in transmitting and distorting sensory signals, in The neurosciences second study program, ed. F. O. Schmitt, Rockefeller University Press, 1970, pp. 597–604
D. Kennedy, Nerve cells and behavior, Amer. Sci. 59, 36–42 (1971)
F. Ratliff, Mach Bands, Holden-Day, New York, 1965
R. Landauer, Cooperative effects, soft models, and fluctuations in data processing, Ferroelectrics 2, 1 (1971)
- Donald E. Knuth, Mathematical analysis of algorithms, Information processing 71 (Proc. IFIP Congress, Ljubljana, 1971) North-Holland, Amsterdam, 1972, pp. 19–27. MR 0403310
- J. F. Traub, Iterative methods for the solution of equations, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0169356
- Bruno Dejon and Peter Henrici (eds.), Constructive aspects of the fundamental theorem of algebra, Wiley-Interscience A Division of John Wiley & Sons, Ltd., London-New York-Sydney, 1969. MR 0253555
R. Landauer, The future evolution of the computer, Physics Today 23, 7, 22 (1970)
R. Keyes, Power dissipation in information processing, Science 168, 796–801, (1970)
M. Freiser and P. Marcus, A survey of some physical limitations on computer elements, IEEE Trans, on Magnetics MAG-5, 82–90 (1969)
- A. G. Vituškin, Otsenka slozhnostn zadachi tabulirovaniya, Sovremennye Problemy Matematiki. Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1959 (Russian). MR 0117486
A. N. Kolmogorov, On the representations of continuous functions of several variables in the form of superposition of continuous functions of one variable and addition, Dokl. Akad. Nauk 114, 679–681 (1957) (Russian)
S. Winograd, On the time required to perform addition, J. Assoc. Comp. Mach. 12, 277–285 (1965)
V. Ya. Pan, Meihods of computing values of polynomials, Uspehi. Mat. Nauk 21, 103–134 (1966) (Russian); English translation in Russian Math. Surveys 21, 105–136 (1966)
- Shmuel Winograd, On the number of multiplications necessary to compute certain functions, Comm. Pure Appl. Math. 23 (1970), 165–179. MR 260150, DOI https://doi.org/10.1002/cpa.3160230204
- Volker Strassen, Gaussian elimination is not optimal, Numer. Math. 13 (1969), 354–356. MR 248973, DOI https://doi.org/10.1007/BF02165411
- S. Winograd and P. Wolfe, On the rate of convergence of local iterative schemes, Theory of machines and computations (Proc. Internat. Sympos., Technion, Haifa, 1971) Academic Press, New York, 1971, pp. 67–70. MR 0455359
- V. V. Kljuev and N. I. Kokovkin-Ščerbak, On the minimization of the number of arithmetic operations for solving linear algebraic systems of equations, Ž. Vyčisl. Mat i Mat. Fiz. 5 (1965), 21–33 (Russian). MR 172453
- W. D. Frazer and A. C. McKellar, Samplesort: A sampling approach to minimal storage tree sorting, J. Assoc. Comput. Mach. 17 (1970), 496–507. MR 287744, DOI https://doi.org/10.1145/321592.321600
An as-yet unpublished result of M. Blum (Berkeley), R. Floyd (Stanford), R. Tarjens (Cornell), and others.
H. Marko, Physikalische und biologische Grenzen der Informationsübermittlung, Kybernetik 2, 274–284 (1965)
H. J. Bremermann, Optimization through evolution and recombination, in Self-organizing systems, edited by M. C. Yovits et al., Spartan Books, Washington, D. C., 1962, pp. 93–106
W. Ashby, Some consequences of Bremermann’s limit for information-processing systems, in Cybernetic problems in bionics, Bionics Symposium, 1966, ed. Hans L. Oestreicher, Gordon and Breach, N. Y., 1968, pp. 69–76
T. von Karman, The engineer grapples with nonlinear problems, Bull. A. M. S. 46, 615 (1940)
T. von Karman, Tooling up mathematics for engineering, Quart. Appl. Math. 1, 1 (1943)
H. Cohen, Mathematics and the biomedical sciences, in The mathematical sciences: a collection of essays, ed. National Research Council’s Committee on Support of Research in the Mathematical Sciences (COSRIMS), The MIT Press, Cambridge, Mass., 1969, pp. 217–231
A. Weyl, Appendix to C. B. Lévi-Strauss, Les structures élémentaires de la parenté, Presses universitaires de France, Paris, 1949
N. Chomsky, Formal properties of grammars, in Handbook of Math. Psych., ed. R. D. Luce, R. R. Bush, and E. Galanter, John Wiley, New York 1963, Vol. 2
D. C. Gazis, A computer model for the financial analysis of urban housing projects, Socio-Econ. Plan. Science 5, 125–144 (1971)
H. Cohen, Nonlinear diffusion problems, in MAA Studies in Mathematics, Vol. 7, Studies in Applied Mathematics, ed. A. H. Taub, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1971, pp. 27–64
R. FitzHugh, Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber, Biophys. J. 2, 11–21 (1962)
W. L. Hardy, Propagation speed in myelinated nerve: dependence on external sodium, Ph.D. dissertation, University of Washington (1969)
R. Stein, The role of spike trains in transmitting and distorting sensory signals, in The neurosciences second study program, ed. F. O. Schmitt, Rockefeller University Press, 1970, pp. 597–604
D. Kennedy, Nerve cells and behavior, Amer. Sci. 59, 36–42 (1971)
F. Ratliff, Mach Bands, Holden-Day, New York, 1965
R. Landauer, Cooperative effects, soft models, and fluctuations in data processing, Ferroelectrics 2, 1 (1971)
D. Knuth, Mathematical analysis of algorithms, IFIP Congress, Ljubljana (1971)
J. Traub, Iterative methods for the solution of equations, Prentice-Hall, Englewood Cliffs, N. J., 1964
B. Dejon and P. Henrici, ed., Constructive aspects of the fundamental theorem of algebra, Proc. of Symp. at IBM Zurich, June 1967, Wiley-Interscience, New York, 1968
R. Landauer, The future evolution of the computer, Physics Today 23, 7, 22 (1970)
R. Keyes, Power dissipation in information processing, Science 168, 796–801, (1970)
M. Freiser and P. Marcus, A survey of some physical limitations on computer elements, IEEE Trans, on Magnetics MAG-5, 82–90 (1969)
A. G. Vitushkin, Estimation of the complexity of the tabulation problem, Fizmatgiz, Moscow, 1959 (Russian); translated: Theory of the transmission and processing on information, Pergamon Press, New York, 1961
A. N. Kolmogorov, On the representations of continuous functions of several variables in the form of superposition of continuous functions of one variable and addition, Dokl. Akad. Nauk 114, 679–681 (1957) (Russian)
S. Winograd, On the time required to perform addition, J. Assoc. Comp. Mach. 12, 277–285 (1965)
V. Ya. Pan, Meihods of computing values of polynomials, Uspehi. Mat. Nauk 21, 103–134 (1966) (Russian); English translation in Russian Math. Surveys 21, 105–136 (1966)
S. Winograd, On the number of multiplications necessary to compute certain functions, Comm. Pure Appl. Math. 23, 165–179 (1970)
V. Strassen, Gaussian elimination is not optimal, Numer. Math. 13, 354–356 (1969)
S. Winograd and P. Wolfe, On the rate of convergence of local iterative schemes, in Theory of Machines and Computations, Academic Press, Inc., N. Y. and London, 1971, pp. 67–70
V. V. Kljuev and N. I. Kokovkin-Shcherbak, On the minimization of the number of arithmetic operations for the solution of linear algebraic systems of equations, Zh. Vychisl. Mat. i Mat. Fiz. 5, 21–23 (1965) (Russian); English translation in U.S.S.R. Comput. Math, and Math. Phys. 5, 25–43 (1965). Also translated in Technical Report CS24, Department of Computer Science, Stanford University (June 1965)
W. Frazer and A. McKellar, Sample sort: a sampling approach to minimal storage-free sorting, J. Assoc. Comp. Mach. 17, 496–507 (1970)
An as-yet unpublished result of M. Blum (Berkeley), R. Floyd (Stanford), R. Tarjens (Cornell), and others.
H. Marko, Physikalische und biologische Grenzen der Informationsübermittlung, Kybernetik 2, 274–284 (1965)
H. J. Bremermann, Optimization through evolution and recombination, in Self-organizing systems, edited by M. C. Yovits et al., Spartan Books, Washington, D. C., 1962, pp. 93–106
W. Ashby, Some consequences of Bremermann’s limit for information-processing systems, in Cybernetic problems in bionics, Bionics Symposium, 1966, ed. Hans L. Oestreicher, Gordon and Breach, N. Y., 1968, pp. 69–76
Additional Information
Article copyright:
© Copyright 1972
American Mathematical Society
