Modular arithmetic for linear algebra computations in the real field

Journal of Symbolic Computation

Volumn 26, Issue 1, 1998, Pages 71-87

  Emiris, Ioannis Z ^a   Pan, Victor Y ^b   Yu, Yanqiang ^c  

^a INRIA   (France)

^b CITY UNIVERSITY OF NEW YORK   (United States)

^c CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032119428     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1998.0201     Document Type: Article

References (25)

1. Atkinson, K.E. (1978). Introduction to Numerical Analysis. Wiley, New York.
2. Aho, A.V., Hopcroft, J.E., Ullman, J.D. (1974). The Design and Analysis of Computer Algorithms. Addison-Wesley.
3. Bini, D., Pan, V.Y. (1994). Polynomial and Matrix Computations, volume 1: Fundamental Algorithms. Birkhäuser, Boston.
4. Brönnimann, H., Emiris, I.Z., Pan, V.Y., Pion, S. (1997). Computing exact geometric predicates using modular arithmetic with single precision. In Proc. ACM Symp. on Computational Geometry, Nice, pp. 174-182.
5. Conte, S.D., de Boor, C. (1980). Elementary Numerical Analysis: An Algorithmic Approach. McGraw Hill.
6. Davenport, J.H., Siret, Y., Tournier, E. (1988). Computer Algebra. Academic Press.
7. Duhamel, P. (1986). Implementation of "Split Radix" FFT algorithms for complex, real and real symmetric data. IEEE Trans. Acoust., Speech, Signal Processing, 34, 285-295.
8. Dahlquist, G., Björck, Å. (1974). Numerical Methods. Prentice-Hall.
9. Emiris, I.Z. (1998). A complete implementation for computing general dimensional convex hulls. Intern. J. Computational Geometry & Applications. To appear. A preliminary version in Tech. Report 2551, INRIA Sophia-Antipolis, France, 1995.
10. Gregory, R.T. (1980). Error-Free Computation: Why It Is Needed and Methods for Doing It. Krieger.
11. Golub, G.H., Van Loan, C.F. (1989). Matrix Computations. Johns Hopkins University Press.
12. Higham, N.J. (1996). Accuracy and Stability of Numerical Algorithms. SIAM Publications.
13. Isaacson, E., Keller, H. (1966). Analysis of Numerical Methods. Wiley.
14. Johnston, R.L. (1982). Numerical Methods : A Software Approach. Wiley.
15. Nussbaumer, H.J. (1980). Fast polynomial transform algorithms for digital convolution. IEEE Trans. on Acoust., Speech, Signal Processing, 28, 205-215.
16. Pan, V.Y. (1991). Complexity of algorithms for linear systems of equations. In Spedicato, E., ed., Computer Algorithms for Solving Linear Algebraic Equations, The State of the Art, NATO ASI Series, Series F: Computer and Systems Sciences, 77, Springer, pp. 27-56.
17. Pan, V.Y. (1992a). Complexity of computations with matrices and polynomials. SIAM Rev., 34, 225-262.
18. Pan, V.Y. (1992b). Can we utilize the cancelation of the most significant digits? Tech. Report TR-92-061, The International Computer Science Institute, Berkeley.
19. Pan, V.Y. (1993). On binary segmentation for matrix and vector operations. Computer and Math. (with Applications), 25, 3, pp. 69-71.
20. Pan, V.Y., Reif, J. (1992). Compact multigrid. SIAM J. on Sci. and Statist. Comp. 13, 119-127.
21. Pan, V.Y., Reif, J. (1993). Generalized compact multigrid. Computer and Math. (with Applications), 25, 35.
22. Varga, R. (1962). Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs.
23. Wilkinson, J.M. (1965). Algebraic Eigenvalue Problem. Clarendon Press.
24. Winograd, S. (1980). Arithmetic Complexity of Computations. SIAM, Philadelphia.
25. Young, D. (1971). Iterative Solutions of Large Linear Systems. Academic Press.