Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
ISCA '89 Proceedings of the 16th annual international symposium on Computer architecture
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Modular arithmetic for linear algebra computations in the real field
Journal of Symbolic Computation
Structured matrices and polynomials: unified superfast algorithms
Structured matrices and polynomials: unified superfast algorithms
Acceleration of Euclidean Algorithm and Rational Number Reconstruction
SIAM Journal on Computing
On Wiedemann's Method of Solving Sparse Linear Systems
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Approximate algorithms to derive exact solutions to systems of linear equations
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
On computing the determinant and Smith form of an integer matrix
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Modern Computer Algebra
Solving structured linear systems with large displacement rank
Theoretical Computer Science
Schur aggregation for linear systems and determinants
Theoretical Computer Science
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
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Our unified superfast algorithms for solving Toeplitz, Hankel, Vandermonde, Cauchy, and other structured linear systems of equations with integer coefficients combine Hensel's symbolic lifting and numerical iterative refinement and run in nearly optimal randomized Boolean time for both solution and its correctness verification. The algorithms and nearly optimal time bounds are extended to some fundamental computations with univariate polynomials that have integer coefficients. Furthermore, we develop lifting modulo powers of two to implement our algorithms in the binary mode within a fixed precision.