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

References | Additional Information

**[1]**Theodore von Kármán,*The engineer grapples with non-linear problems*, Bull. Amer. Math. Soc.**46**(1940), 615–683. MR**0003131**, https://doi.org/10.1090/S0002-9904-1940-07266-0**[2]**T. von Karman,*Tooling up mathematics for engineering*, Quart. Appl. Math.**1**, 1 (1943)**[3]***The mathematical sciences: A collection of essays*, 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, The M.I.T. Press, Cambridge, Mass.-London, 1969. MR**0235955****[4]**A. Weyl, Appendix to C. B. Lévi-Strauss,*Les structures élémentaires de la parenté*, Presses universitaires de France, Paris, 1949**[5]**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**[6]**D. C. Gazis,*A computer model for the financial analysis of urban housing projects*, Socio-Econ. Plan. Science**5**, 125-144 (1971)**[7]**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****[8]**R. FitzHugh,*Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber*, Biophys. J.**2**, 11-21 (1962)**[9]**W. L. Hardy,*Propagation speed in myelinated nerve: dependence on external sodium*, Ph.D. dissertation, University of Washington (1969)**[10]**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**[11]**D. Kennedy,*Nerve cells and behavior*, Amer. Sci.**59**, 36-42 (1971)**[12]**F. Ratliff,*Mach Bands*, Holden-Day, New York, 1965**[13]**R. Landauer,*Cooperative effects, soft models, and fluctuations in data processing*, Ferroelectrics**2**, 1 (1971)**[14]**Donald E. Knuth,*Mathematical analysis of algorithms*, Information processing 71 (Proc. IFIP Congress, Ljubljana, 1971) North-Holland, Amsterdam, 1972, pp. 19–27. MR**0403310****[15]**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****[16]***Constructive aspects of the fundamental theorem of algebra*, Proceedings of a Symposium Conducted at the IBM Research Laboratory, Zürich-Rüschlikon, June 5-7, vol. 1967, Wiley-Interscience A Division of John Wiley & Sons, Ltd., London-New York-Sydney, 1969. MR**0253555****[17]**R. Landauer,*The future evolution of the computer*, Physics Today**23**, 7, 22 (1970)**[18]**R. Keyes,*Power dissipation in information processing*, Science**168**, 796-801, (1970)**[19]**M. Freiser and P. Marcus,*A survey of some physical limitations on computer elements*, IEEE Trans, on Magnetics**MAG-5**, 82-90 (1969)**[20]**A. G. Vituškin,*\cyr Otsenka slozhnostn zadachi tabulirovaniya*, Sovremennye Problemy Matematiki. Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1959 (Russian). MR**0117486****[21]**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)**[22]**S. Winograd,*On the time required to perform addition*, J. Assoc. Comp. Mach.**12**, 277-285 (1965)**[23]**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)**[24]**Shmuel Winograd,*On the number of multiplications necessary to compute certain functions*, Comm. Pure Appl. Math.**23**(1970), 165–179. MR**0260150**, https://doi.org/10.1002/cpa.3160230204**[25]**Volker Strassen,*Gaussian elimination is not optimal*, Numer. Math.**13**(1969), 354–356. MR**0248973**, https://doi.org/10.1007/BF02165411**[26]**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****[27]**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**0172453****[28]**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**0287744**, https://doi.org/10.1145/321592.321600**[29]**An as-yet unpublished result of M. Blum (Berkeley), R. Floyd (Stanford), R. Tarjens (Cornell), and others.**[30]**H. Marko,*Physikalische und biologische Grenzen der Informationsübermittlung*, Kybernetik**2**, 274-284 (1965)**[31]**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**[32]**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

DOI:
https://doi.org/10.1090/qam/99736

Article copyright:
© Copyright 1972
American Mathematical Society