Efficient Algorithms for Computing the Nearest Polynomial with a Real Root and Related Problems

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn 1999-January, Issue , 1999, Pages 205-212

  Hitz, Markus A ^a   Kaltofen, Erich ^b   Lakshman, Y N ^c  

^a UNIVERSITY OF NORTH GEORGIA   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

^c LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005459699     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/309831.309937     Document Type: Conference Paper

References (21)

1. CORLESS, R. M., GIANNI, P. M., TRAGER, B. M., AND WATT, S. M. The singular value decomposition for polynomial systems. In Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation, ISSAC'95 (1995), pp. 195-207.
2. DEMMEL, J. W. On condition numbers and the distance to the nearest ill-posed problem. Numerische Mathematik 51 (1987), 251-289.
3. ECKART, C., AND YOUNG, G. The approximation of one matrix by another of lower rank. Psychometrika 1, 3 (Sept. 1936), 211-218.
4. GALLIGO, A., AND WATT, S. A numerical absolute primality test for bivariate polynomials. In ISSAC 97 Proc. 1997 Internat. Symp. Symbolic Alqebraic Comput. (New York, K. Y., 1997), W. Küchlin, Ed., ACM Press, pp. 217-224.
5. HITZ, M. Porting computer algebra algorithms to numerical computing - the difficult case. SIGSAM Bulletin 30, 1 (Mar. 1996), 44-45. ECCAD'96 abstract.
6. HITZ, M. A. Efficient Algoritfnns for Computing the Nearest Polynomial with Constrained Roots. PhD thesis, Rensselaer Polytechnic Institute, Troy, N.Y., 1998.
7. HITZ, M. A., AND KALTOFEN, E. Efficient algorithms for computing the nearest polynomial with constrained roots. In Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation, IS-SAC'98 (1998), pp. 236-243.
8. HOUGH, D. G. Explaining and ameliorating the ill condition of zeros of polynomials. PhD thesis, University of California, Berkeley, C.A., 1977.
9. KAHAN, W. Numerical linear algebra. Canadian Math. Dull. 9 (1966). 757-801.
10. KALTOFEN, E. Fast parallel absolute irreducibility testing. J. Symbolic Comput. 1, 1 (1985), 57-67.
11. Misprint corrections: J. Symbolic Comput. vol. 9, p. 320 (1989).
12. KALTOFEN, E. Polynomial factorization 1987-1991. In Proc. LATIN '92 (Heidelberg New York, 1992), I. Simon, Ed., vol. 583 of Lect. Notes Comput. Sci., Springer, pp. 294-313.
13. KARMARKAR, N., AND LAKSHMAN Y. N. Approximate polynomial greatest common divisors and nearest singular polynomials. In Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, ISSAC'96 (1996), pp. 35-39.
14. KARMARKAK, N. K., AND LAKSHMAN, Y. N. On approximate GCDs of univariate polynomials. J. Symbolic Comput. 26, 6 (1998), 653-666. Special issue on Symbolic Numeric Algebra for Polynomials S. M. Watt and H. J. Stetter, editors.
15. LIPPERT, R. A., AND EDELMAN, A. The computation and sensitivity of double eigenvalues. Manuscript; see link at http://www-math.mit.edu/~edelman/, Jan. 1998.
16. MANOCHA, D., AND DEMMEL, J. Algorithms for intersecting parametric and algebraic curves II: Multiple intersections. Computer Vision. Graphics and Image Processing: Graphical Models and Image Processing 57, 2 (1995), 81-100.
17. POLJAK, S., AND ROHN, J. Checking robust nonsin-gularitv is NP-hard. Math. Control Signals Systems 6 (1993), 1-9.
18. STIEFEL, E. Uber diskrete und lineare Tschebyscheff-Approximationen. Numerische Mathematik 1 (1959), 1-28.
19. STIEFEL, E. Note on Jordan elimination, linear programming, and Tschebyscheff approximationen. Numerische Mathematik 2 (1960), 1-17.
20. VAN DOOREN, P., AND VERMAUT, V. On stability radii of generalized eigenvalue problems. In Proc. European Conference on Control (1997).
21. WILKINSON, J. H. The perfidious polynomial. In Studies in Numerical Analysis, G. H. Golub, Ed., vol. 24 of Studies in Mathematics, M.A.A., 1984, pp. 1-28.