On the complexity of skew arithmetic

In this paper, we study the complexity of several basic operations on linear differential operators with polynomial coefficients. As in the case of ordinary polynomials, we show that these complexities can be expressed almost linearly in terms of the cost of multiplication.

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Vydáno v:Applicable algebra in engineering, communication and computing Ročník 27; číslo 2; s. 105 - 122
Hlavní autor: van der Hoeven, Joris
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2016
Témata:
Artificial Intelligence
Computer Hardware
Computer Science
Original Paper
Symbolic and Algebraic Manipulation
Theory of Computation
68Q15
68W30
Multiplication
12E15
Local solution
34M03
Division
lclm
Linear differential operators
Algorithm
gcrd
Complexity
ISSN:0938-1279, 1432-0622
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Popis
Shrnutí:In this paper, we study the complexity of several basic operations on linear differential operators with polynomial coefficients. As in the case of ordinary polynomials, we show that these complexities can be expressed almost linearly in terms of the cost of multiplication.
ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-015-0269-0