- 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 Scholar
- 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 Scholar
- 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 Scholar
- 4 BAREISS, E.H. Sylvester's iclentity and multistep integer preserving Gaussian elimination. Math. Comput. 22, 103 (Jul. 1968), 565-578.Google Scholar
- 5 BARETSS, E. H. Computational solution of matrix problems over an integral domain. J. Inst. Math. Appl. 10, I (Aug. 1972), 68-104.Google Scholar
- 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 Scholar
- 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 Scholar
- 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 Scholar
- 9 CHu4 C.K. Multivariate Splines. SIAM, Philadelphia, 1988.Google Scholar
- 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 Scholar
- 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 Scholar
- 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 Scholar
- 13 GOLUB, G. H., AND VAN LOAN, C.F. Matrix Computations. Johns Hopkins University Press, Baltimore, 1983.Google Scholar
- 14 GONNET, G.H. Handbook of Algorithms and Data Structures. Addison Wesley, Reading, Mass., 1984. Google Scholar
- 15 GREGORY, R. T., AND KRIS~NAMURT~IY, E. V. Methods and Applications of Error-Free Computation. Springer Verlag, Berlin, 1984. Google Scholar
- 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 Scholar
- 17 HEARN, A.C. REDUCE User's Manual, Version 3.1. The Rand Corporation, Santa Monica, Calif., 1984.Google Scholar
- 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 Scholar
- 19 HOWELL, J. A., AND GREGORY, R.T. Solving linear equations using residue arithmetic--algorithm II. BIT 10, 1 (Spring 1970), 27-37.Google Scholar
- 20 KNUTH, D. E. The Art of Computer Programming, Vol. 2.' Seminumerical Algorithms. Addison Wesley, Reading, Mass., 1969. Google Scholar
- 21 KRISHNAMURTHY, E. V Error-Free Polynomial Matrix Computations. Springer Verlag, Berlin, 1985. Google Scholar
- 22 LYCHE, T., AND SCHUMAKER, L. L. Ed. Mathematical Methods ~n Computer A~ded Geometric Design. Academic Press, San Diego, Calif. 1989. Google Scholar
- 23 NEWMAN, M. 167; Solving equations exactly. J. Res. Natl. Bur. Stand. Sect. B, 17 (Oct.-Dec. 1967), 171-179.Google Scholar
- 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 Scholar
- 25 RIESEL, H Prime Nambers and Computer Methods for Factorization. Birkh~user Verlag, 1985. Google Scholar
- 26 SEDGEWICK, R. Algorithms. Addison Wesley, Reading, Mass., 1983. Google Scholar
- 27 SPRINGER, J. Exact solution of general integer systems of linear equations. ACM Trans. Math. Softw. 12, (1986), 51-61. Google Scholar
- 28 STALLINGS, W. T AND BOUILLION, T. L. Computation of pseudo-inverse matrices using residue arithmetic. SIAM Rev. 14, (1972), 152-163.Google Scholar
Index Terms
- The exact analysis of sparse rectangular linear systems
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