Ideal Bases and Primary Decomposition: Case of Two Variables
Journal of Symbolic Computation
A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Solving systems of nonlinear polynomial equations faster
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
The inverses of block Hankel and block Toeplitz matrices
SIAM Journal on Computing
On fast multiplication of polynomials over arbitrary algebras
Acta Informatica
A reliable method for computing M-Pade´ approximants on arbitrary staircases
Journal of Computational and Applied Mathematics
A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants
SIAM Journal on Matrix Analysis and Applications
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Asymptotically fast solution of Toeplitz-like singular linear systems
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Mathematics of Computation
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Structured matrices and polynomials: unified superfast algorithms
Structured matrices and polynomials: unified superfast algorithms
Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs
SIAM Journal on Matrix Analysis and Applications
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
Improved Sparse Multivariate Polynomial Interpolation Algorithms
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Finite field linear algebra subroutines
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
On the complexity of polynomial matrix computations
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Fast algorithms for multivariable systems.
Fast algorithms for multivariable systems.
Modern Computer Algebra
The aggregation and cancellation techniques as a practical tool for faster matrix multiplication
Theoretical Computer Science - Algebraic and numerical algorithm
Solving sparse rational linear systems
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Solving structured linear systems with large displacement rank
Theoretical Computer Science
Computing specified generators of structured matrix inverses
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
| Hi-index | 0.01 |
Linear systems with structures such as Toeplitz-, Vandermonde-or Cauchy-likeness can be solved in O~(α2n) operations, where n is the matrix size, α is its displacement rank, and O~denotes the omission of logarithmic factors. We show that for Toeplitz-like and Vandermonde-like trices, this cost can be reduced to O~(αω--1 n), where ω is a feasible exponent for matrix multiplication over the base field. The best known estimate for ω is ωO~(α1.38n). We also present consequences for Hermite-Padé approximation and bivariate interpolation.