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Arithmetic complexity of the Stirling transforms
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Sergey B. Gashkov
Published/Copyright:
April 17, 2015
Abstract
For the linear Stirling transforms of both kinds, which are well-known in combinatorics, we obtain close to optimal estimates of the complexity of computation by vector addition chains and non-branching programs composed of arithmetic operations over real numbers. A relation between these problems and the Lagrange and Newton interpolation is discussed.
Keywords: Stirling transforms of the 1st and 2nd kinds; addition vector chains; circuits in arithmetic bases; the Lagrange and Newton interpolation; Vandermonde matrices; the Gauss q-binomial coefficient
Received: 2014-6-1
Published Online: 2015-4-17
Published in Print: 2015-4-1
© 2015 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Weighing algorithms of classification and identification of situations
- Arithmetic complexity of the Stirling transforms
- Asymptotics of the logarithm of the number of (k, l)-sum-free sets in an Abelian group
- Multiplicative complexity of some Boolean functions
- On a statistic for testing the homogeneity of polynomial samples
Articles in the same Issue
- Frontmatter
- Weighing algorithms of classification and identification of situations
- Arithmetic complexity of the Stirling transforms
- Asymptotics of the logarithm of the number of (k, l)-sum-free sets in an Abelian group
- Multiplicative complexity of some Boolean functions
- On a statistic for testing the homogeneity of polynomial samples
