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The exact analysis of sparse rectangular linear systems

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Published:01 December 1991Publication History
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  1. 1 ALFELD, P. A case study of multivariate piecewise polynomials. In Geometric Modeling: Algorithms and New Trends, G. E. Farin, Ed., SIAM, Philadelphia, 1986, 149-159.Google ScholarGoogle Scholar
  2. 2 ALFELD, P., AND EYRE, D. J. Algorithm 701: Goliath: A software system for the exact analysis of rectangular rank-deficient sparse rational linear systems. Collected Algorithms of the ACM.Google ScholarGoogle Scholar
  3. 3 ALFELD, P., EYRE, D. J., AND SCHUMAKER, L.L. Machine aided investigation of multivarL ate spline spaces. In Approximation Theory V/, C. K. Chui, L. L. Schumaker and J. D. Ward Eds., Academic Press, San Diego, 1989, 1-4.Google ScholarGoogle Scholar
  4. 4 BAREISS, E.H. Sylvester's iclentity and multistep integer preserving Gaussian elimination. Math. Comput. 22, 103 (Jul. 1968), 565-578.Google ScholarGoogle Scholar
  5. 5 BARETSS, E. H. Computational solution of matrix problems over an integral domain. J. Inst. Math. Appl. 10, I (Aug. 1972), 68-104.Google ScholarGoogle Scholar
  6. 6 BoRos~, I., AND FRAENKEL, A. S. Exact solutions of linear equations with rational coefficients by congruence techniques. Math. Comput. 20, 93 (Jan. 1966), 107-112.Google ScholarGoogle Scholar
  7. 7 CABAY, S., AND LAM, T. P. L. Congruence techniques for the exact solution of integer systems of linear equations. ACM Trans. Math. Softw. 3, 4 (Dec. 1977), 386-397. Google ScholarGoogle Scholar
  8. 8 CABAY, S., AND LAM, T. P. L. ESOLVE: Congruence techniques for the exact solution of integer systems of linear equations. ACM Trans. Math. Softw. 3, 4 (Dec. 1977), 404-410 Google ScholarGoogle Scholar
  9. 9 CHu4 C.K. Multivariate Splines. SIAM, Philadelphia, 1988.Google ScholarGoogle Scholar
  10. 10 DONGARRA, J. J., AND GROSSE, E. Distribution of mathematical software via electronic mail. Numerical Analysis Manuscript 85-2, AT&T Bell Laboratories, Murray Hill, N.J., 1985.Google ScholarGoogle Scholar
  11. 11 EYRE, D. J. Exact analysis of sparse rectangular linear systems. M.S. thesis, Dept. of Mathematics, Univ. of Utah, Salt Lake City, 1990.Google ScholarGoogle Scholar
  12. 12 FRAENK~L, A. S., ANn LOEWENTHAL, D Exact solution of linear equations with rational coefflcients; J. Res. Natl. Bur. Stand. 75B, i and 2 (Jan.-Jun. 1971), 67-75.Google ScholarGoogle Scholar
  13. 13 GOLUB, G. H., AND VAN LOAN, C.F. Matrix Computations. Johns Hopkins University Press, Baltimore, 1983.Google ScholarGoogle Scholar
  14. 14 GONNET, G.H. Handbook of Algorithms and Data Structures. Addison Wesley, Reading, Mass., 1984. Google ScholarGoogle Scholar
  15. 15 GREGORY, R. T., AND KRIS~NAMURT~IY, E. V. Methods and Applications of Error-Free Computation. Springer Verlag, Berlin, 1984. Google ScholarGoogle Scholar
  16. 16 GRISS, M.L. The Algebraic solution of large sparse systems using REDUCE 2. In Proceedings ACM 74 (San Diego, Calif., 1974) 105-111. Google ScholarGoogle Scholar
  17. 17 HEARN, A.C. REDUCE User's Manual, Version 3.1. The Rand Corporation, Santa Monica, Calif., 1984.Google ScholarGoogle Scholar
  18. 18 HOWELL, J. A., AND GREGORY, R. T. An algorithm for solving linear algebraic equations using residue arithmetic, I-II. BIT 9, 3 (Fall 1969), 200-224, 324-337.Google ScholarGoogle Scholar
  19. 19 HOWELL, J. A., AND GREGORY, R.T. Solving linear equations using residue arithmetic--algorithm II. BIT 10, 1 (Spring 1970), 27-37.Google ScholarGoogle Scholar
  20. 20 KNUTH, D. E. The Art of Computer Programming, Vol. 2.' Seminumerical Algorithms. Addison Wesley, Reading, Mass., 1969. Google ScholarGoogle Scholar
  21. 21 KRISHNAMURTHY, E. V Error-Free Polynomial Matrix Computations. Springer Verlag, Berlin, 1985. Google ScholarGoogle Scholar
  22. 22 LYCHE, T., AND SCHUMAKER, L. L. Ed. Mathematical Methods ~n Computer A~ded Geometric Design. Academic Press, San Diego, Calif. 1989. Google ScholarGoogle Scholar
  23. 23 NEWMAN, M. 167; Solving equations exactly. J. Res. Natl. Bur. Stand. Sect. B, 17 (Oct.-Dec. 1967), 171-179.Google ScholarGoogle Scholar
  24. 24 RAO, T M., SUBRAMANIAN, K., AND KRISHNAMURTHY, E.V. Residue arithmetic algorithms for exact computation of g-inverses of matrices SIAM J. Numer. Anal. 13 (1976), 155-171.Google ScholarGoogle Scholar
  25. 25 RIESEL, H Prime Nambers and Computer Methods for Factorization. Birkh~user Verlag, 1985. Google ScholarGoogle Scholar
  26. 26 SEDGEWICK, R. Algorithms. Addison Wesley, Reading, Mass., 1983. Google ScholarGoogle Scholar
  27. 27 SPRINGER, J. Exact solution of general integer systems of linear equations. ACM Trans. Math. Softw. 12, (1986), 51-61. Google ScholarGoogle Scholar
  28. 28 STALLINGS, W. T AND BOUILLION, T. L. Computation of pseudo-inverse matrices using residue arithmetic. SIAM Rev. 14, (1972), 152-163.Google ScholarGoogle Scholar

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        cover image ACM Transactions on Mathematical Software
        ACM Transactions on Mathematical Software  Volume 17, Issue 4
        Dec. 1991
        118 pages
        ISSN:0098-3500
        EISSN:1557-7295
        DOI:10.1145/210232
        Issue’s Table of Contents

        Copyright © 1991 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 December 1991
        Published in toms Volume 17, Issue 4

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