Essentially optimal computation of the inverse of generic polynomial matrices

Authors:
Claude-Pierre Jeannerod;Gilles Villard
Affiliations:
CNRS, INRIA, Laboratoire LIP, École Normale Supérieure de Lyon, 46, Allée d'Italie 69364 Lyon Cedex 07, France;CNRS, INRIA, Laboratoire LIP, École Normale Supérieure de Lyon, 46, Allée d'Italie 69364 Lyon Cedex 07, France
Venue:
Journal of Complexity - Special issue: Foundations of computational mathematics 2002 workshops
Year:
2005

Citing 16
Cited 6

A new method for computing a column reduced polynomial matrix

Systems & Control Letters
On fast multiplication of polynomials over arbitrary algebras

Acta Informatica
On computing determinants of matrices without divisions

ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants

SIAM Journal on Matrix Analysis and Applications
Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems

Mathematics of Computation
An algorithm for inverting rational matrices

Systems & Control Letters
Modern computer algebra

Modern computer algebra
Shifted normal forms of polynomial matrices

ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Approximate algorithms to derive exact solutions to systems of linear equations

EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
High-order lifting

Proceedings of the 2002 international symposium 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
Chinese remainder and interpolation algorithms

SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
On the complexity of polynomial matrix computations

ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
On lattice reduction for polynomial matrices

Journal of Symbolic Computation
High-order lifting and integrality certification

Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Normal forms for general polynomial matrices

Journal of Symbolic Computation

Computing the rank and a small nullspace basis of a polynomial matrix

Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Some recent progress in exact linear algebra and related questions

Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Efficient network code design for cyclic networks

IEEE Transactions on Information Theory
Computing hermite forms of polynomial matrices

Proceedings of the 36th international symposium on Symbolic and algebraic computation
Computing minimal nullspace bases

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Creative telescoping for rational functions using the griffiths: dwork method

Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation

Quantified Score

Hi-index	0.06

Visualization

Abstract

We present an inversion algorithm for nonsingular n × n matrices whose entries are degree d polynomials over a field. The algorithm is deterministic and, when n is a power of two, requires O ∼ (n3d) field operations for a generic input; the soft-O notation O∼ indicates some missing log(nd) factors. Up to such logarithmic factors, this asymptotic complexity is of the same order as the number of distinct field elements necessary to represent the inverse matrix.