Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On fast multiplication of polynomials over arbitrary algebras
Acta Informatica
Fast algorithms for Taylor shifts and certain difference equations
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Modern computer algebra
FFT-like multiplication of linear differential operators
Journal of Symbolic Computation
The aggregation and cancellation techniques as a practical tool for faster matrix multiplication
Theoretical Computer Science - Algebraic and numerical algorithm
Polynomial evaluation and interpolation on special sets of points
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Chebyshev expansions for solutions of linear differential equations
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Fast algorithms for differential equations in positive characteristic
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
On Computing the Hermite Form of a Matrix of Differential Polynomials
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Optimization techniques for small matrix multiplication
Theoretical Computer Science
Fast computation of common left multiples of linear ordinary differential operators
ACM Communications in Computer Algebra
Fast computation of common left multiples of linear ordinary differential operators
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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It 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.