On fast multiplication of polynomials over arbitrary algebras
- D. Cantor, E. Kaltofen
- Computer Science, MathematicsActa Informatica
- 1 October 1991
This paper generalizes the well-known Sch6nhage-Strassen algorithm for multiplying large integers to an algorithm for dividing polynomials with coefficients from an arbitrary, not necessarily commutative, not always associative, algebra d, and obtains a method not requiring division that is valid for any algebra.
Subquadratic-time factoring of polynomials over finite fields
- E. Kaltofen, V. Shoup
- Computer Science, MathematicsSymposium on the Theory of Computing
- 29 May 1995
New probabilistic algorithms are presented for factoring univariate polynomials over finite fields, using fast matrix multiplication techniques and the new baby step/giant step techniques.
On Wiedemann's Method of Solving Sparse Linear Systems
- E. Kaltofen, B. D. Saunders
- Computer ScienceInternational Symposium on Applied Algebra…
- 7 October 1991
Douglas Wiedemann’s (1986) landmark approach to solving sparse linear systems over finite fields provides the symbolic counterpart to non-combinatorial numerical methods for solving sparse linear…
Analysis of Coppersmith's Block Wiedemann Algorithm for the Parallel Solution of Sparse Linear Systems
- E. Kaltofen
- Computer ScienceInternational Symposium on Applied Algebra…
- 10 May 1993
It is proved that by use of certain randomizations on the input system the parallel speed up is roughly by the number of vectors in the blocks when using as many processors.
Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators
- E. Kaltofen, B. Trager
- Computer Science, Mathematics[Proceedings ] 29th Annual Symposium on…
- 24 October 1988
Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. It is…
On the complexity of computing determinants
- E. Kaltofen, G. Villard
- Mathematics, Computer ScienceComputational Complexity
- 1 September 2001
New baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems that deterministically compute the determinant, characteristic polynomial and adjoint of A with n3.2+o(1) and O(n2.697263) ring additions, subtractions and multiplications are presented.
Factorization of Polynomials Given by Straight-Line Programs
- E. Kaltofen
- Computer Science, MathematicsAdvances in Computational Research
- 1989
This paper can probabilistically determine all those sparse irreducible factors of a polynomial given by a straight-line program that have less than a given number of monomials.
Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials
- E. Kaltofen, Zhengfeng Yang, L. Zhi
- Mathematics, Computer ScienceInternational Symposium on Symbolic and Algebraic…
- 9 July 2006
This work presents an algorithm based on a version of the structured total least norm (STLN) method and demonstrates that the algorithm in practice computes globally minimal approximations on a diverse set of benchmark polynomials.
Improved Sparse Multivariate Polynomial Interpolation Algorithms
- E. Kaltofen, Y. N. Lakshman
- Computer Science, MathematicsInternational Symposium on Symbolic and Algebraic…
- 4 July 1988
This work considers the problem of interpolating sparse multivariate polynomials from their values and presents efficient algorithms for finding the rank of certain special Toeplitz systems arising in the Ben-Or and Tiwari algorithm and for solving transposed Vandermonde systems of equations.
On approximate irreducibility of polynomials in several variables
- E. Kaltofen, Jon P. May
- MathematicsInternational Symposium on Symbolic and Algebraic…
- 3 August 2003
Using an absolute irreducibility criterion due to Ruppert, this work is able to find useful separation bounds, in several norms, for bivariate polynomials, and derive new, more effective Noether forms for polynmials of arbitrarily many variables.
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