Keywords
- Fast Fourier Transform
- Tridiagonal Matrix
- Cyclic Reduction
- Tridiagonal System
- Alamos Scientific Laboratory
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9. References
Richard Bellman, Introduction to Matrix Analysis, McGraw-Hill, New York, 1960.
Oscar Buneman, Stanford University Institute for Plasma Research, Report No.294, 1969.
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.)
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.
F.W. Dorr, "The direct solution to the discrete Poisson equation on a rectangle," to appear in SIAM Review.
J.A. George, "An Embedding Approach to the Solution of Poisson’s Equation on an Arbitrary Bounded Region," to appear as a Stanford Report.
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).
R.W. Hockney, "A fast direct solution of Poisson’s equation using Fourier analysis," J. ACM., Vol.12 No.1 (1965), pp. 95–113.
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.
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.
R.S. Varga, Matrix Interative Analysis, Prentice Hall, New York, 1962.
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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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