Higher Order Aitken Extrapolation with Application to Converging and Diverging Gauss-Seidel Iterations

Show more

References

[1] H. L. Stone, “Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations,” SIAM Journal on Numerical Analysis, Vol. 5, No. 3, 1968, pp. 530-558. http://dx.doi.org/10.1137/0705044

[2] M. R. Hestenes and E. Stiefel, “Methods of Conjugate Gradients for Solving Linear Systems,” Journal of Research at the National Bureau of Standards, Vol. 49, 1952, pp. 409-436. http://dx.doi.org/10.6028/jres.049.044

[3] G. H. Golub and C. F. Van Loan, “Matrix Computations,” 3 Edition, Johns Hopkins University Press, Baltimore, 1996.

[4] J. C. West, “Preconditioned Iterative Solution of Scattering from Rough Surfaces,” IEEE Transactions on Antennas and Propagation, Vol. 48, No. 6, 2000, pp. 1001-1002. http://dx.doi.org/10.1109/8.865236

[5] A. C. Aitken, “Studies in Practical Mathematics. The Evaluation of Latent Roots and Latent Vectors of a Matrix,” Proceedings of the Royal Society of Edinburgh, Vol. 57, 1937, p. 269.

[6] M. D. Gianola and L. R. Schaffer, “Extrapolation and Convergence Criteria with Jacobi and Gauss-Seidel Iteration in Animal Models,” Journal of Diary Science, Vol. 70, No. 12, 1987, pp. 2577-2584.

[7] B. Irons and N. G. Shrive, “Numerical Methods in Engineering and Applied Science: Numbers are Fun,” John Wiley & Sons, New York, 1987.

[8] S. R. Capehart, “Techniques for Accelerating Iterative Methods for the Solution of Mathematical Problems,” Ph.D. Dissertation, Oklahoma State University, 1989.

[9] P. Henrici, “Elements of Numerical Analysis,” John Wiley & Sons, New York, 1964.

[10] S. D. Kamvar, T. H. Haveliwala, C. D. Manning and G. H. Golub, “Extrapolation Methods for Accelerating Page Rank Computations,” Proceedings of the Twelfth International World Wide Web Conference, 2003, pp. 261-270.

http://dx.doi.org/10.1145/775152.775190

[11] C. Breziniski and M. R. Zaglia, “Generalizations of Aitken’s Process for Accelerating the Convergence of Sequences,” Journal of Computational and Applied Mathematics, Vol. 26, No. 2, 2007, pp. 171-189.

[12] A. Bjorck, “Numerical Methods in Scientific Computing,” Linkoping University Royal Institute of Technology, Vol. 2, 2009.

[13] D. M. Young, “Iterative Solution of Large Linear Systems,” Academic Press, New York, 1971.

[14] G. Dahlquist and A. Bjorck, “Numerical Methods,” Prentice Hall, Englewood Cliffs, 1974.

[15] C. F. Gerald and P. O. Wheatley, “Applied Numerical Analysis,” 5th Edition, 1994.

[16] L. A. Hageman and D. M. Young, “Applied Iterative Methods,” Academic Press, New York, 1981.