On the equivalence between Berlekamp's and Euclid's algorithms
IEEE Transactions on Information Theory
A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
SIAM Journal on Computing
Power series remainder sequences and Padé fractions over an integral domain
Journal of Symbolic Computation
Computational Complexity of Sparse Rational Interpolation
SIAM Journal on Computing
Algorithms for computing sparse shifts for multivariate polynomials
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
FOXBOX: a system for manipulating symbolic objects in black box representation
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Mathematics for the Analysis of Algorithms
Mathematics for the Analysis of Algorithms
A Zero-Test and an Interpolation Algorithm for the Shifted Sparse Polynominals
AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Early termination strategies in sparse interpolation algorithms
Early termination strategies in sparse interpolation algorithms
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
ACM Communications in Computer Algebra
On the matrix berlekamp-massey algorithm
ACM Transactions on Algorithms (TALG)
A computer algebra user interface manifesto
ACM Communications in Computer Algebra
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As a sub-procedure our algorithm executes the Berlekamp/Massey algorithm on a sequence of large integers or polynomials. We give a fraction-free version of the Berlekamp/Massey algorithm, which does not require rational numbers or functions and GCD operations on the arising numerators and denominators. The relationship between the solution of Toeplitz systems, Padé approximations, and the Euclidean algorithm is classical. Fraction-free versions [3] can be obtained from the subresultant PRS algorithm [2]. Dornstetter [6] gives an interpretation of the Berlekamp/Massey algorithm as a partial extended Euclidean algorithm. We map the subresultant PRS algorithm onto Dornstetter's formulation. We note that the Berlekamp/Massey algorithm is more efficient than the classical extended Euclidean algorithm.