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Iterative solution of linear and nonlinear systems derived from elliptic partial differential equations

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References

  1. Varga, R. S., Matrix Iterative Analysis, Prentice-Hall, New Jersey, 1962.

    Google Scholar 

  2. Wachspress, E. L., Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics, Prentice-Hall, New Jersey, 1966.

    MATH  Google Scholar 

  3. Young, D. M., Iterative Solution of Large Linear Systems, Academic Press, New York, 1971.

    MATH  Google Scholar 

  4. Young, D. M., On the consistency of linear stationary iterative methods, SIAM J. Numer. Anal. 9 (1972), 89–96.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Golub, G. H., and R. S. Varga, Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second-order Richardson iterative methods, Numer. Math., Parts I and II, 3 (1961), 146–168.

    CrossRef  MATH  Google Scholar 

  6. Young, M., A bound on the optimum relaxation factor for the successive overrelaxation method, Numer. Math. 16 (1971), 408–413.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Young, D. M., Solution of linear systems of equations, in Numerical Solutions of Partial Differential Equations J. G. Gram, ed.), D. Reidel Publishing Co., Holland, 1974. (Proceedings of Conference “Advanced Study Institute on Numerical Solution of Partial Differential Equations,” Kjeller, Norway, Aug. 20–24, 1973).

    Google Scholar 

  8. Young, D. M., “On the accelerated SSOR method for solving large linear systems,” to appear in Advances in Mathematics (to appear also in a special volume dedicated to Professor Garrett Birkhoff of Harvard University on the occasion of his 65th birthday.

    Google Scholar 

  9. Diamond, M. A., An economical algorithm for the solution of finite difference equations, Report UIUC DCS-R-71-492, Department of Computer Science, Univ. of Illinois at Urbana-Champaign, Illinois, 1971.

    Google Scholar 

  10. Hageman, L. A., and David M. Young, Stopping criteria and adaptive parameter estimation for certain iterative procedures, in preparation.

    Google Scholar 

  11. Hageman, L. A., The estimation of acceleration parameters for the Chebyshev polynomial and the successive overrelaxation iteration methods, Report WAPD-TM-1038, Bettis Atomic Power Laboratory, Westinghouse Electric Corp., Pittsburgh, Pa., 1972.

    Google Scholar 

  12. Cullen, Charles, Dynamic parameter determination with the Jacobi semiiterative method, in preparation.

    Google Scholar 

  13. Sheldon, J., On the numerical solution of elliptic difference equations, Math. Tables Aids Comput. 9 (1955), 101–112.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Habetler, G. J., and E. L. Wachspress, Symmetric successive overrelaxation in solving diffusion difference equations, Math. Comp. 15 (1961), 356–362.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Ehrlich, L. W., The block symmetric successive overrelaxation method, J. SIAM 12 (1964), 807–826.

    MathSciNet  MATH  Google Scholar 

  16. Axelsson, O., A generalized SSOR method, BIT 13 (1972), 443–467.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Axelsson, O., Generalized SSOR methods, Report DD/72/8 CERN-Data Handling Divison, Geneva, 1972.

    Google Scholar 

  18. Axelsson, O., On preconditioning and convergence acceleration in sparse matrix problems, CERN 74-10, May 8, 1974, Geneva, Switzerland.

    Google Scholar 

  19. Young, D. M., Second-degree iterative methods for the solution of large linear systems, J. Approx. Theory 5 (1972), 137–148.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Young, D. M., On the accelerated SSOR method for solving elliptic boundary value problems, in Lecture Notes in Mathematics (A. Dold and B. Eckmann, eds.), Vol. 363, Conference on the Numerical Solution of Differential Equations, Dundee, 1973 (G. A. Watson, ed.), Springer-Verlag, New York, 1974.

    Google Scholar 

  21. Benokraitis, V. J., On the Adaptive Acceleration of Symmetric Successive Over-relaxation, doctoral thesis, University of Texas, Austin, 1974.

    Google Scholar 

  22. Nichols, Nancy K., On the convergence of two-stage iterative processes for solving linear equations, SIAM J. Numer. Anal. 10 (1973), 460–469.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. Young, D. M., and Mary F. Wheeler, Alternating direction methods for solving partial difference equations, in Nonlinear Problems in Engineering (W. F. Ames, ed.), Academic Press, New York, 1964, 220–246.

    CrossRef  Google Scholar 

  24. Ortega, J., and W. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.

    MATH  Google Scholar 

  25. Ames, W. F., Nonlinear Partial Differential Equations in Engineering, Academic Press, New York, 1965.

    MATH  Google Scholar 

  26. Ames, W. F., Numerical Methods for Partial Differential Equations, Barnes and Noble, New York, 1969.

    MATH  Google Scholar 

  27. Schechter, Samuel, Relaxation methods for convex problems, SIAM J. Numer. Anal. 5 (1968), 601–612.

    CrossRef  MathSciNet  MATH  Google Scholar 

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Young, D.M. (1975). Iterative solution of linear and nonlinear systems derived from elliptic partial differential equations. In: Oden, J.T. (eds) Computational Mechanics. Lecture Notes in Mathematics, vol 461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074157

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  • DOI: https://doi.org/10.1007/BFb0074157

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