Distributed Matrix-Free Solution of Large Sparse Linear Systems over Finite Fields

Algorithmica (New York)

Volumn 24, Issue 3, 1999, Pages 331-348

  Kaltofen, E ^a   Lobo, A ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b WASHINGTON COLLEGE   (United States)

Author keywords

Block Wiedemann; Distributed symbolic computation; Outer loop parallelization; Sparse linear systems

Indexed keywords

EID: 0002404842     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00008266     Document Type: Article

References (21)

1. Beckerman, B., and Lahahn, G. A uniform approach for the fast computation of matrix-type Padé approximants. SIAM J. Matrix Anal. Appl. 15(3) (1994), 804-823.
2. Berlekamp, E. R. Algebraic Coding Theory. McGraw-Hill, New York, 1968.
3. Bitmead, R. R., and Anderson, B. D. O. Asymptotically fast solution of Toeplitz and related systems of linear equations. Linear Algebra Appl. 34 (1980), 103-116.
4. Coppersmith, D. Solving linear systems over GF(2). Tech. Report RC 16997, IBM Thomas J. Watson Research Center, NY, 1991.
5. Gohberg, I., Kailath, T., and Koltracht, I. Efficient solution of linear systems of equations with recursive structure. Linear Algebra Appl. 80 (1986), 81-113.
6. Golliver, R. A., Lenstra, A. K., and McCurley, K. S. Lattice sieving and trial division. In Proc. ANTS '94 (1994).
7. Kailath, T., Kung, S. Y., and Morf, M. Displacement ranks of matrices and linear equations. Linear Algebra Appl. 80 (1979), 395-407.
8. Kaltofen, E. Efficient solution of sparse linear systems. Lecture notes, Dept. of Computer Science, Rensselaer Polytechnic Institute, Troy, NY.
9. Kaltofen, E. Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems. Tech. Report 93-22, Rensselaer Polytechnic Institute, Troy, NY, 1993.
10. Kaltofen, E., and Pan, V. Processor-efficient parallel solution of linear systems over an abstract field. In Proc. 3rd Annual ACM Symp. Parallel Algorithms and Architectures, ACM Press, New York, 1991, pp. 180-191.
11. Krylov, A. N. On the numerical solution of the equation by which the frequency of small oscillations is determined in technical problems (in Russian). Izv. Akad. Nauk SSSR Ser. Fiz.-Mat. 4 (1931), 491-539.
12. LaMacchia, B. A., and Odlyzko, A. M. Solving large sparse linear systems over finite fields. In Advances in Cryptology: CRYPTO '90 (1990), pp. 109-133.
13. Lenstra, A. K., and Manasse, M. S. Factoring by electronic mail. In Proc. Eurocrypt '89 (1990), pp. 355-371.
14. Massey, J. L. Shift-register synthesis and BCH decoding. IEEE Trans. Inform. Theory 15 (1969), 122-127.
15. Morf, M. Doubling algorithms for Toeplitz and related equations. In Proc. IEEE Internat. Conf. Acoustics, Speech, and Signal Processing. IEEE, New York, 1980, pp. 954-959.
16. Pomerance, C., and Smith, J. W. Reduction of huge sparse matrices over finite fields via created catastrophes. Experiment. Math. 1 (1992), 89-94.
17. Rissanen, J. Realizations of matrix sequences. Tech. Report RJ-1032, IBM, Yorktown Heights, NY, 1972.
18. Rivest, R. L., Shamir, A., and Adleman, L. A method for obtaining digital signatures and public-key cryptosystems. Comm. ACM 21 (1978), 120-126.
19. Rosenbrock, H. H. State-Space and Multivariable Theory. Wiley, New York, 1970.
20. Villard, G. Further analysis of Coppersmith's block Wiedemann algorithm for the solution of sparse linear systems. In Proc. ISSAC '97 (Hawaii), ACM Press, New York, 1997, pp. 205-211.
21. Wiedemann, D. Solving sparse linear equations over finite fields. IEEE Trans. Inform. Theory 32 (1986), 54-62.