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Direct methods for solving elliptic difference equations

Part of the Lecture Notes in Mathematics book series (LNM,volume 193)

Keywords

  • Fast Fourier Transform
  • Tridiagonal Matrix
  • Cyclic Reduction
  • Tridiagonal System
  • Alamos Scientific Laboratory

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9. References

  1. Richard Bellman, Introduction to Matrix Analysis, McGraw-Hill, New York, 1960.

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  2. Oscar Buneman, Stanford University Institute for Plasma Research, Report No.294, 1969.

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  3. B.L. Buzbee, G.H. Golub and C.W. Nielson, "The Method of Odd/Even Reduction and Factorization with Application to Poisson’s Equation, Part II," LA-4288, Los Alamos Scientific Laboratory. (To appear SIAM J. Num. Anal.)

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  4. J.W. Cooley and J.W. Tukey, "An algorithm for machine calcualtion of complex Fourier series," Math. Comp., Vol.19, No.90 (1965), pp. 297–301.

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  5. F.W. Dorr, "The direct solution to the discrete Poisson equation on a rectangle," to appear in SIAM Review.

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  7. G.H. Golub, R. Underwood and J. Wilkinson, "Solution of \(A\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x} = \lambda B\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x}\) when B is positive definite," (to be published).

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  8. R.W. Hockney, "A fast direct solution of Poisson’s equation using Fourier analysis," J. ACM., Vol.12 No.1 (1965), pp. 95–113.

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  9. R.W. Hockney, in Methods in Computational Physics (B. Adler, S. Fernbach and M. Rotenberg, Eds.), Vol.9 Academic Press, New York and London, 1969.

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  10. R.E. Lynch, J.R. Rice and D.H. Thomas, "Direct solution of partial difference equations by tensor product methods," Num. Math., Vol.6 (1964), pp. 185–199.

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  11. R.S. Varga, Matrix Interative Analysis, Prentice Hall, New York, 1962.

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© 1971 Springer-Verlag

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Golub, G. (1971). Direct methods for solving elliptic difference equations. In: Morris, J.L. (eds) Symposium on the Theory of Numerical Analysis. Lecture Notes in Mathematics, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060341

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  • DOI: https://doi.org/10.1007/BFb0060341

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05422-1

  • Online ISBN: 978-3-540-36538-9

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