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Some structural theorems for partial difference operators

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References

  1. Young, D. M.: Iterative methods for solving partial difference equations of elliptic type. Trans. Amer. Math. Soc.76, 92–111 (1954).

    Google Scholar 

  2. Varga, R. S.: Matrix iterative analysis. Englewood Cliffs, New Jersey: Prentice-Hall, Inc. 1962.

    Google Scholar 

  3. Forsythe, G. E., andW. R., Wasow: Finite difference methods for partial differential equations. New York: John Wiley and Sons, Inc. 1960.

    Google Scholar 

  4. Roth, J.: An application of algebraic topology: Kron's method of tearing. Quart. Appl. Math.17, 1–25 (1959).

    Google Scholar 

  5. Kron, G.: A set of principles to interconnect the solutions of physical problems. J. Appl. Phys.24, 71–97 (1953).

    Google Scholar 

  6. Ehrlick, L. W.: The block symmetric successive overrelaxation method. University of Texas thesis 1963.

  7. Todd, J., ed.: Survey of numerical analysis. New York: McGraw-Hill 1962.

    Google Scholar 

  8. Engeli, M., T. Ginsberg, H. Ruthishauser, andE. Stiefel: Refined iterative methods for computation of the solution and the eigenvalues of self adjoint boundary value problems. Mitteilungen aus dem Institut für angewandte Mathematik, Nr. 8. Basel: Birkhauser 1959.

    Google Scholar 

  9. Bourgin, D. G.: Modern algebraic topology. New York and London: MacMillan 1963.

    Google Scholar 

  10. Lyusternik, L. A.: On difference approximations of the Laplace operator. Uspehi. Mat. Nauk (N.S.)9 (1954), translated in Amer. Math. Soc. Trans., Series 2,8, 289–351 (1958).

  11. Gantmacher, F. R.: Applications of the theory of matrices, translated and revised byJ. L. Brenner. New York: Interscience (John Wiley and Sons Inc.) 1959.

    Google Scholar 

  12. Harary, F.: A graph theoretic method for the complete reduction of a matrix with a view toward finding its eigenvalues. J. Math. and Phys.38 104–111 (1959).

    Google Scholar 

  13. —: On the consistency of precedence matrices. J. Assoc. Comput. Mach.7, 255–259 (1960).

    Google Scholar 

  14. Heller, J.: Ordering properties of linear successive iteration schemes applied to multi-diagonal type linear systems. J. Soc. Indust. Appl. Math.5, 238–243 (1957).

    Google Scholar 

  15. Parter, S. V.: The use of linear graphs in Gauss elimination. SIAM Rev.3, 119–130 (1961).

    Google Scholar 

  16. Harary, F.: The number of linear, directed, rosted, and connected graphs. Trans. Amer. Math. Soc.78, 445–463 (1955).

    Google Scholar 

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Authors and Affiliations

  1. Purdue University, 47907, Lafayette, Indiana, USA

    J. S. Maybee

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  1. J. S. Maybee
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This work was done while the author was supported by the National Science Foundation Grant G-19019 at Oregon State University, Corvallis, Oregon.

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Maybee, J.S. Some structural theorems for partial difference operators. Numer. Math. 7, 66–72 (1965). https://doi.org/10.1007/BF01397973

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