International audienceIt is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than the previously-known one by a constant factor, and prove that in characteristic zero, multiplication of differential operators and of matrices are computationally equivalent problems. In positive characteristic, we show that differential operators can be multiplied in nearly optimal time. Theoretical results are validated by intensive experiments
This "habilitation à diriger des recherches" manuscript concerns the efficiency in exact linear alge...
Motivated by studying the power of randomness, certifying algorithms and barriers for fine-grained r...
International audienceFor matrices with displacement structure, basic operations like multiplication...
International audienceWe show that linear differential operators with polynomial coefficients can be...
AbstractWe give complexity estimates for the problems of evaluation and interpolation on various pol...
AbstractIt is well known that integers or polynomials can be multiplied in an asymptotically fast wa...
13 pagesIn this paper, we study the complexity of several basic operations on linear differential op...
A theorem of N. Katz (1990) [Ka], p. 45, states that an irreducible differential operator L over a s...
AbstractComputing the coefficients of the characteristic polynomial is about as hard as matrix multi...
International audienceThis paper describes an algorithm which computes the characteristic polynomial...
AbstractA classical theorem of Stafford says: every left ideal of partial differential operators wit...
AbstractLet A be a matrix whose entries are indeterminates over an infinite field. It is shown that,...
Structured linear algebra techniques are a versatile set of tools; they enable one to deal at once w...
AbstractIn the straight-line program model, it is known that computing all partial derivatives of a ...
International audienceWe consider the problem of computing univariate polynomial matrices over afiel...
This "habilitation à diriger des recherches" manuscript concerns the efficiency in exact linear alge...
Motivated by studying the power of randomness, certifying algorithms and barriers for fine-grained r...
International audienceFor matrices with displacement structure, basic operations like multiplication...
International audienceWe show that linear differential operators with polynomial coefficients can be...
AbstractWe give complexity estimates for the problems of evaluation and interpolation on various pol...
AbstractIt is well known that integers or polynomials can be multiplied in an asymptotically fast wa...
13 pagesIn this paper, we study the complexity of several basic operations on linear differential op...
A theorem of N. Katz (1990) [Ka], p. 45, states that an irreducible differential operator L over a s...
AbstractComputing the coefficients of the characteristic polynomial is about as hard as matrix multi...
International audienceThis paper describes an algorithm which computes the characteristic polynomial...
AbstractA classical theorem of Stafford says: every left ideal of partial differential operators wit...
AbstractLet A be a matrix whose entries are indeterminates over an infinite field. It is shown that,...
Structured linear algebra techniques are a versatile set of tools; they enable one to deal at once w...
AbstractIn the straight-line program model, it is known that computing all partial derivatives of a ...
International audienceWe consider the problem of computing univariate polynomial matrices over afiel...
This "habilitation à diriger des recherches" manuscript concerns the efficiency in exact linear alge...
Motivated by studying the power of randomness, certifying algorithms and barriers for fine-grained r...
International audienceFor matrices with displacement structure, basic operations like multiplication...