Approximate square-free decomposition and root-finding of lll-conditioned algebraic equations
Journal of Information Processing
Journal of Information Processing
Lattice basis reduction: improved practical algorithms and solving subset sum problems
Mathematical Programming: Series A and B
On approximate GCDs of univariate polynomials
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Approximate polynomial Gcds, Padé approximation, polynomial zeros and bipartite graphs
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Computation of approximate polynomial GCDs and an extension
Information and Computation
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
The Complexity of Approximate Optima for Greatest Common Divisor Computations
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Approximate Integer Common Divisors
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Heuristics on lattice basis reduction in practice
Journal of Experimental Algorithmics (JEA)
Approximate factorization of multivariate polynomials via differential equations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
The approximate GCD of inexact polynomials
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
A Rank-Revealing Method with Updating, Downdating, and Applications
SIAM Journal on Matrix Analysis and Applications
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Computers & Mathematics with Applications
Approximate polynomial gcd: small degree and small height perturbations
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Approximate polynomial gcd: Small degree and small height perturbations
Journal of Symbolic Computation
IEEE Transactions on Signal Processing
QR factoring to compute the GCD of univariate approximate polynomials
IEEE Transactions on Signal Processing
An improvement in the lattice construction process of approximate polynomial GCD over integers
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
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Symbolic numeric algorithms for polynomials are very important, especially for practical computations since we have to operate with empirical polynomials having numerical errors on their coefficients. Recently, for those polynomials, a number of algorithms have been introduced, such as approximate univariate GCD and approximate multivariate factorization for example. However, for polynomials over integers having coefficients rounded from empirical data, changing their coefficients over reals does not remain them in the polynomial ring over integers; hence we need several approximate operations over integers. In this paper, we discuss computing a polynomial GCD of univariate or multivariate polynomials over integers approximately. Here, ''approximately'' means that we compute a polynomial GCD over integers by changing their coefficients slightly over integers so that the input polynomials still remain over integers.