Journal Article10.1109/PROC.1972.8746
A new algorithm for factoring polynomials
L. Tessler,Larry Eisenberg +1 more
- 01 Jun 1972
- Vol. 60, Iss: 6, pp 737-738
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TL;DR: A new algorithm for finding the roots of polynomials is presented that is reliable, rapid, has a high order of convergence, and excellent convergence in the large.
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Abstract: A new algorithm for finding the roots of polynomials is presented. The method is based upon an accurate first approximation to a root which is then used to initiate an iterative solution. The method is reliable, rapid, has a high order of convergence, and excellent convergence in the large.
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Citations
Subquadratic-time factoring of polynomials over finite fields
Erich Kaltofen,Victor Shoup +1 more
- 29 May 1995
TL;DR: New probabilistic algorithms are presented for factoring univariate polynomials over finite fields, using fast matrix multiplication techniques and new “baby step/giant step” techniques.
Polynomial Factorization
TL;DR: A new coefficient bound is established for factoring univariate polynomials over the integers that is derived from the weighted norm introduced in Beauzamy et al. (1990) and is almost optimal.
49
Composition collisions and projective polynomials: statement of results
Joachim von zur Gathen,Mark Giesbrecht,Konstantin Ziegler +2 more
- 25 Jul 2010
TL;DR: This work investigates the decomposition of polynomials whose degree is a power of p. and presents certain decompositions and conjecture that these comprise all of the prescribed shape.
17
Connections between the algorithms of Berlekamp and Niederreiter for factoring polynomials over Fq
TL;DR: An explicit isomorphism is determined between the solution spaces of Berlekamp's and Niederreiter's algorithm for factoring polynomials over finite fields that can be used for the implementation of a procedure combining the benefits of both methods.
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References
A Machine Method for Solving Polynomial Equations
TL;DR: It is tame to consider methods of more uniform solutions to the problem of finding numerical approximations to the roots of a polynomial that may be far too laborious to carry out by hand but which nevertheless are sufficiently easy for an automatic computer.
89
Polynomial factorization using the routh criterion
E.J. Mastascusa,W.C. Rave,B.M. Turner +2 more
- 01 Sep 1971
TL;DR: Experimental results indicate that the method used for polynomial factorization is competitive with several common algorithms on both the accuracy and the computation time basis.
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