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A Family of Permutations for Concurrent Factorization of Block Tridiagonal Matrices
June 1989 (vol. 38 no. 6)
pp. 812-824
The inherent strong seriality of closely coupled systems is circumvented by defining a family of permutations for reordering equation sets whose matrix of coefficients is Hermitian block tridiagonal. The authors show how these permutations can be used to achieve relatively high concurrency in the Cholesky factorization of banded systems at the expense of introducing limited extra computations d

[1] J. H. Wilkinson,The Algebraic Eigenvalue Problem. London, England: Oxford University Press, 1965.
[2] F. Akyuz and S. Utku, "An automatic node-relabelling scheme for bandwidth minimization of stiffness matrices,"AIAA J., vol. 6, pp. 728-730, 1968.
[3] J. A. George and J. Liu,Computer Solution of Large Sparse Positive Definite Systems. Englewood Cliffs, NJ: Prentice-Hall, 1981.
[4] S. Utku, M. Salama, and R. Melosh, "Concurrent Cholesky factorization of positive definite banded Hermitian matrices,"Int. J. Numer. Methods Eng., vol. 23, pp. 2137-2152, 1986.
[5] S. Utku, M. Salama, and R. Melosh, "Parallel solution of closely coupled systems,"Int. J. Numer. Methods Eng., vol. 23, pp. 2177-2186, 1986.
[6] D. Heller, "Some aspects of the cyclic reduction algorithm for block tridiagonal linear systems,"SIAM J. Numer. Anal., vol. 13, pp. 484-496, 1976.
[7] S. L. Johnson, "Solving narrow banded systems on ensemble architectures,"ACM Trans. Math. Software, vol. 11, pp. 271-288, 1985.
[8] J. M. Ortega and R. G. Voigt,Solution of Partial Differential Equations on Vector and Parallel Computers. Philadelphia, PA: SIAM, 1985.

Index Terms:
permutations; concurrent factorization; block tridiagonal matrices; closely coupled systems; equation sets; Hermitian block tridiagonal; Cholesky factorization; speedup; efficiency; computational complexity; matrix algebra; parallel algorithms.
Citation:
S. Utku, M. Salama, R.J. Melosh, "A Family of Permutations for Concurrent Factorization of Block Tridiagonal Matrices," IEEE Transactions on Computers, vol. 38, no. 6, pp. 812-824, June 1989, doi:10.1109/12.24290
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