Digital-Computer-Oriented Numerical Analysis In Surface Chemistry

  • J. Adin MannJr.


Why write on numerical analysis methods in a series dedicated to methods for the study of surface effects? My point is that coupled with a computer, numerical methods allow us to handle the information “explosion” created by modern instrumental techniques and our own “need to know” about the structure and function of surfaces. It is probably easiest to expand on this statement with a short discussion of only one application of the methods to be outlined in this article.


Loss Function Model Function Matrix Method Risk Function Error Level 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. A. Bouchiat and J. Meunier, Phys. Rev. Lett. 23 (14), 752 (1969).CrossRefGoogle Scholar
  2. 2.
    R. Deutsch, Estimation Theory, Prentice-Hall, Englewood Cliffs, N.J., 1965.Google Scholar
  3. 3.
    B. N. Taylor, W. H. Parker, and D. N. Langenberg, The Fundamental Constants and Quantum Electrodynamics, Academic Press, New York, 1969.Google Scholar
  4. 4.
    P. R. Halmos, Measure Theory, Van Nostrand Co., Princeton, New Jersey, 1950.Google Scholar
  5. 5.
    R. Deutsch, Estimation Theory, Prentice-Hall, Englewood Cliffs, N.J., 1965, p. 10.Google Scholar
  6. 6.
    W. Feller, An Introduction to Probability Theory and Its Applications, John Wiley and Sons, New York, 1950.Google Scholar
  7. 7.
    W. E. Wentworth, J. Chem. Ed. 42, 96 (1965).CrossRefGoogle Scholar
  8. 8.
    J. R. Wolberg, Prediction Analysis,Van Nostrand Co., Princeton, N.J., 1967. These formulas are derived in more detail in Chap. 3. In comparing equations given above with Wolberg’s Eqs. (3.6.5) and (3.6.22), it would appear that one of us has an incorrect sign. This is not the case, since my 0 and Wolberg’s A are defined with opposite signs. Note also the convention he used in identifying the residues with the powers of the Taylor’s series. Wolberg’s Chap. 4, “Prediction Analysis,” is most interesting.Google Scholar
  9. 9.
    K. E. Iverson, A Programming Language, John Wiley and Sons, New York, 1962.Google Scholar
  10. 10.
    For a definition of the language, see the IBM users manual, APL LANGUAGE, identified as GC26–3847–2 available from any branch office of IBM. See also L. Gilman and A. J. Rose, Apl an Interactive Approach ( 2nd ed. ), John Wiley and Sons, New York, 1976.Google Scholar
  11. 11.
    A. Virj, J. Coll. Interface Sci. 19, 1 (1964).Google Scholar
  12. 12.
    A. B. Delfino, M.S. thesis, University of Hawaii, Honolulu, Hawaii, 1965.Google Scholar
  13. 13.
    J. T. Golden, FORTRAN IV Programming and Computers, Prentice-Hall, Englewood Cliffs, N.J., 1965.Google Scholar
  14. G. Forsythe and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, Englewood Cliffs, N.J., 1967.Google Scholar
  15. 14.
    D. J. Wilde, Optimum Seeking Methods,Prentice Hall, Englewood Cliffs, N.J., 1964. See p. 145 for the pattern search.Google Scholar
  16. 15.
    R. Hooke and T. A. Jeeves, J. Assoc. Comp. Mach. 8, 212 (1961).CrossRefGoogle Scholar
  17. For an application of this method, see R. G. Anthony and D. M. Himmelblau, J. Phys. Chem. 67, 1080 (1963).CrossRefGoogle Scholar
  18. 16.
    H. Margenau and G. M. Murphy, The Mathematics of Physics and Chemistry ( 2nd ed. ), Van Nostrand and Co., Princeton, N.J., 1965;Google Scholar
  19. G. Rutledge, Phys. Rev. 40, 262 (1932).CrossRefGoogle Scholar
  20. 17.
    R. S. Hansen, J. Lucassen, R. L. Bendure, and G. Bierwagen, J. Colloid and Interface Sci. 26, 198 (1968).CrossRefGoogle Scholar
  21. 18.
    R. S. Hansen and J. A. Mann, J. Appl. Phys. 35, 152 (1964).CrossRefGoogle Scholar
  22. 19.
    M. Van den Temple and van de Riet, J. Chem. Phys. 42, 2769 (1965).CrossRefGoogle Scholar
  23. 20.
    Chapter 4 of this volume.Google Scholar
  24. 21.
    G. Du, “Ripple Wave Theoretical Model Studies,” M.S. thesis, University of Hawaii, Honolulu, Hawaii, 1969.Google Scholar
  25. 22.
    B. W. Ninham, V. A. Parsegian, and G. H. Weiss, J. Stat. Phys. 2, 323 (1970);CrossRefGoogle Scholar
  26. V. A. Parsegian and B. W. Ninham, J. Coll. Interface Sci. 37, 332 (1971).CrossRefGoogle Scholar
  27. 23.
    R. Beckett and J. Hurt, Numerical Calculations and Algorithms, McGraw-Hill Book Co., New York, 1967;Google Scholar
  28. D. D. McCracken and W. S. Forn, Numerical Methods and FORTRAN Programming, John Wiley and Sons, New York, 1964;Google Scholar
  29. A. Ralston, A First Course in Numerical Analysis, McGraw-Hill Book Co., New York, 1965;Google Scholar
  30. J. Todd (ed.), Survey of Numerical Analysis, McGraw-Hill Book Co., New York, 1956;Google Scholar
  31. K. S. Kunz, Numerical Analysis, McGraw-Hill Book Co., New York, 1957;Google Scholar
  32. C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N.J., 1971.Google Scholar
  33. 24.
    A. D. Whalen, Detection of Signals in Noise, Academic Press, New York, 1971.Google Scholar
  34. 25.
    R. V. Edwards, F. Kucera, J. A. Mann, J. Gertler, S. Herndon, and T. Gall, “Implementation of an APL Driven Laboratory Interface,” Proceedings of APL79, Association of Computing Machinery (1979);Google Scholar
  35. J. A. Mann, R. V. Edwards, T. Gall, H. M. Cheung, F. Cotsfield, C. Havens, and P. Wagner, “APL Level Languages for Analysis,” in Minicomputers and Large Scale Computation, ACS Symposium Series, 57, 41–64 (1977).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • J. Adin MannJr.
    • 1
  1. 1.Department of Chemical EngineeringCase Western Reserve UniversityClevelandUSA

Personalised recommendations