Univariate polynomials: Nearly optimal algorithms for numerical factorization and root-finding

Journal of Symbolic Computation

Volumn 33, Issue 5, 2002, Pages 701-733

  Pan, Victor Y ^a  

^a CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036334966     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.2002.0531     Document Type: Article

References (69)

1. Polynomial and Linear Control Systems
2. The Development of Mathematics
3. Design, analysis, and implementation of a multiprecision polynomial rootfinder
4. Computations with infinite Toeplitz matrices and polynomials
5. Time Series Analysis: Forecasting and Control
6. A History of Mathematics
7. Fast solution of Toeplitz systems of equations and computation of Padé approximations
8. Stability of methods for solving Toeplitz systems of equations
9. Roots of a polynomial and its derivatives
10. A numerical method for locating zeros of an analytic function
11. The Euclid algorithm and the fast computation of cross-covariance and autocovariance sequences
12. A Newton-Raphson method for moving-average spectral factorization using the Euclid algorithm
13. Numerical univariate polynomial GCD
14. Certified approximate polynomial gcds
15. Polynomial root finding using iterated eigenvalue computation
16. Differenzenrechnung, Deutsher Verlag Der Wissenschaften
17. A generalized Graeffe's iteration for evaluating polynomials and rational functions
18. The Padé table and its relation to certain algorithms of numerical analysis
19. The simultaneous improvement of a complete set of approximate factors of a polynomial
20. Applied and Computational Complex Analysis 1
21. Elimination Methods: An Introduction, Symbolic and Numerical Computation for Artificial Intelligence
22. Multiplication of multidigit numbers on automata
23. Polynomial root-finding algorithms and branched covers
24. Fast computation of numerical partial fraction decompositions and contour integrals of rational functions
25. Polynomial factorization and partial fraction decomposition by simultaneous Newton's iteration
26. A fast and stable algorithm for splitting polynomials
27. Tangent Groeffe iteration
28. Bibliography on roots of polynomials
29. A supplementary bibliography on roots of polynomials
30. An inequality about factors of polynomials
31. Asymptotic acceleration of solving polynomial systems
32. Multivariate polynomials, duality and structured matrices
33. Specified precision polynomial root isolation is NC
34. l+ε) algorithm for the complex root problem
35. An efficient algorithm for the complex roots problem
36. Sequential and parallel complexity of approximate evaluation of polynomial zeros
37. Optimal (up to polylog factors) sequential and parallel algorithms for approximating complex polynomial zeros
38. Deterministic improvement of complex polynomial factorization based on the properties of the associated resultant
39. Optimal and nearly optimal algorithms for approximating polynomial zeros
40. Solving a polynomial equation: Some history and recent progress
41. Approximate polynomial gcds, Padé approximation, polynomial zeros, and bipartite graphs
42. Approximating complex polynomial zeros: Modified quadtree (Weyl's) construction and improved Newton's iteration
43. Structured Matrices and Polynomials: Unified Superfast Algorithms
44. Univariate polynomials: Nearly optimal algorithms for factorization and rootfinding
45. Computation of approximate polynomial GCD's and an extension
46. Univariate polynomila root-finding with a lower computational precision and higher convergence rates
47. Can we optimize Toeplitz/Hankel computations?
48. The complexity of the matrix eigenproblem
49. Aufgaben und Lehrsätze aus der Analysis
50. On the worst-case arithmetic complexity of approximating zeros of polynomials
51. The quadtree and related hierarchical data structures
52. Asymptotically fast algorithms for the numerical multiplication and division of polynomials with complex coefficients
53. Quasi-gcd computations
54. Variations on computing reciprocals of power series
55. Schnelle multiplikation grosse Zahlen
56. A quadtree algorithm for template matching on pyramid computer
57. The fundamental theorem of algebra and complexity theory
58. On the efficiency of algorithms of analysis
59. Some numerical challenges in control theory
60. Randbemerkungen zu Hauptproblemen der Mathematik, II, Fundamentalsatz der Algebra and Grundlagen der Mathematik
61. Factorization of the covariance generating function of a pure moving-average process