research-article

FFT-like Multiplication of Linear Differential Operators

Author:

Joris Van Der HoevenAuthors Info & Claims

Journal of Symbolic Computation, Volume 33, Issue 1

Pages 123 - 127

https://doi.org/10.1006/jsco.2000.0496

Published: 01 January 2002 Publication History

Abstract

It is well known that integers or polynomials can be multiplied in an asymptotically fast way using the discrete Fourier transform. In this paper, we give an analogue of fast Fourier multiplication in the ring of skew polynomials Cx, where =x x. More precisely, we show that the multiplication problem of linear differential operators of degree n in x and degree n in can be reduced to the n n matrix multiplication problem.

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Watt S(2023)Efficient Quotients of Non-commutative PolynomialsComputer Algebra in Scientific Computing10.1007/978-3-031-41724-5_20(370-392)Online publication date: 28-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-41724-5_20
Giesbrecht MHuang QSchost ÉChyzak FLabahn G(2021)Sparse Multiplication of Multivariate Linear Differential OperatorsProceedings of the 2021 International Symposium on Symbolic and Algebraic Computation10.1145/3452143.3465527(155-162)Online publication date: 18-Jul-2021
https://dl.acm.org/doi/10.1145/3452143.3465527
Hoeven J(2016)On the complexity of skew arithmeticApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-015-0269-027:2(105-122)Online publication date: 1-Mar-2016
https://dl.acm.org/doi/10.1007/s00200-015-0269-0
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Index Terms

FFT-like Multiplication of Linear Differential Operators
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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cover image Journal of Symbolic Computation

Journal of Symbolic Computation Volume 33, Issue 1

01/01/2002

123 pages

ISSN:0747-7171

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Academic Press, Inc.

United States

Publication History

Published: 01 January 2002

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Watt S(2023)Efficient Quotients of Non-commutative PolynomialsComputer Algebra in Scientific Computing10.1007/978-3-031-41724-5_20(370-392)Online publication date: 28-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-41724-5_20
Giesbrecht MHuang QSchost ÉChyzak FLabahn G(2021)Sparse Multiplication of Multivariate Linear Differential OperatorsProceedings of the 2021 International Symposium on Symbolic and Algebraic Computation10.1145/3452143.3465527(155-162)Online publication date: 18-Jul-2021
https://dl.acm.org/doi/10.1145/3452143.3465527
Hoeven J(2016)On the complexity of skew arithmeticApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-015-0269-027:2(105-122)Online publication date: 1-Mar-2016
https://dl.acm.org/doi/10.1007/s00200-015-0269-0
Bostan AChyzak FSalvy BLi Zvan der Hoeven Jvan Hoeij M(2012)Fast computation of common left multiples of linear ordinary differential operatorsProceedings of the 37th International Symposium on Symbolic and Algebraic Computation10.1145/2442829.2442847(99-106)Online publication date: 22-Jul-2012
https://dl.acm.org/doi/10.1145/2442829.2442847
Bostan AChyzak FLi ZSalvy B(2011)Fast computation of common left multiples of linear ordinary differential operatorsACM Communications in Computer Algebra10.1145/2016567.201658145:1/2(111-112)Online publication date: 25-Jul-2011
https://dl.acm.org/doi/10.1145/2016567.2016581
Drevet CNazrul Islam MSchost É(2011)Optimization techniques for small matrix multiplicationTheoretical Computer Science10.1016/j.tcs.2010.12.012412:22(2219-2236)Online publication date: 1-May-2011
https://dl.acm.org/doi/10.1016/j.tcs.2010.12.012
Bostan ASchost ÉJohnson JPark HKaltofen E(2009)Fast algorithms for differential equations in positive characteristicProceedings of the 2009 international symposium on Symbolic and algebraic computation10.1145/1576702.1576712(47-54)Online publication date: 28-Jul-2009
https://dl.acm.org/doi/10.1145/1576702.1576712
Benoit ASalvy BJohnson JPark HKaltofen E(2009)Chebyshev expansions for solutions of linear differential equationsProceedings of the 2009 international symposium on Symbolic and algebraic computation10.1145/1576702.1576709(23-30)Online publication date: 28-Jul-2009
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Bostan AChyzak FLe Roux NSendra JGonzalez-Vega L(2008)Products of ordinary differential operators by evaluation and interpolationProceedings of the twenty-first international symposium on Symbolic and algebraic computation10.1145/1390768.1390775(23-30)Online publication date: 20-Jul-2008
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Giesbrecht MZhang YHong H(2003)Factoring and decomposing ore polynomials over F(t)Proceedings of the 2003 international symposium on Symbolic and algebraic computation10.1145/860854.860888(127-134)Online publication date: 3-Aug-2003
https://dl.acm.org/doi/10.1145/860854.860888

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Research on FFT-Based Large Integers Multiplication

The Tangent FFT

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