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Fast algorithms for elementary operations on complex power series
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I. S. Sergeev
Published/Copyright:
March 18, 2010
Abstract
It is shown that the inversion of a complex-valued power series can be realised asymptotically with complexity of 5/4 multiplications (if we compare the upper bounds). It is shown that the calculation of the square root requires asymptotically also no more than 5/4 multiplications, the computation of an exponential has the complexity equal to 13/6 multiplications, and raising to an arbitrary power requires 41/12 multiplications.
Received: 2009-04-29
Published Online: 2010-03-18
Published in Print: 2010-March
© de Gruyter 2010
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Articles in the same Issue
- On approximation of continuous functions by determinate functions with delay
- Fast algorithms for elementary operations on complex power series
- On the complexity of the ℰ2 Grzegorczyk class
- On the linear complexity of binary sequences on the basis of biquadratic and sextic residue classes
- On bounds for complexity of circuits of multi-input functional elements
- Upper and lower bounds for the complexity of the branch and bound method for the knapsack problem
- On the finite near-rings generated by endomorphisms of an extra-special 2-group
