Polynomial evaluation and interpolation on special sets of points

Authors:
Alin Bostan;Éric Schost
Affiliations:
Laboratoire STIX, École polytechnique, 91128 Palaiseau, France;Laboratoire STIX, École polytechnique, 91128 Palaiseau, France
Venue:
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Year:
2005

Citing 18
Cited 8

On fast multiplication of polynomials over arbitrary algebras

Acta Informatica
Hypergeometric solutions of linear recurrences with polynomial coefficients

Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
An FFT extension of the elliptic curve method of factorization

An FFT extension of the elliptic curve method of factorization
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
Greatest factorial factorization and symbolic summation

Journal of Symbolic Computation
Computing Popov and Hermite forms of polynomial matrices

ISSAC '96 Proceedings of the 1996 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
Modern computer algebra

Modern computer algebra
Challenges of symbolic computation: my favorite open problems

Journal of Symbolic Computation
Fast computation of linear generators for matrix sequences and application to the block Wiedemann algorithm

Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Subquadratic computation of vector generating polynomials and improvement of the block Wiedemann algorithm

Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
High-order lifting

Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Tellegen's principle into practice

ISSAC '03 Proceedings of the 2003 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
The Middle Product Algorithm I

Applicable Algebra in Engineering, Communication and Computing
Fast modular transforms via division

SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
Fast modular transforms

Journal of Computer and System Sciences

Basis-Independent Polynomial Division Algorithm Applied to Division in Lagrange and Bernstein Basis

Computer Mathematics
An efficient algorithm for multivariate Maclaurin-Newton transformation

Annales UMCS, Informatica
Newton's method and FFT trading

Journal of Symbolic Computation
Chebyshev interpolation polynomial-based tools for rigorous computing

Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Cryptanalysis of the RSA subgroup assumption from TCC 2005

PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Genus 2 point counting over prime fields

Journal of Symbolic Computation
Power series solutions of singular (q)-differential equations

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Algorithms for the universal decomposition algebra

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We give complexity estimates for the problems of evaluation and interpolation on various polynomial bases. We focus on the particular cases when the sample points form an arithmetic or a geometric sequence, and we discuss applications, respectively, to computations with linear differential operators and to polynomial matrix multiplication.