Fast computation of multinomial coefficients

In a previous publication, we have used the discrete Fourier transform to compute the binomial coefficients. In the present paper, we extend the previously proposed method to compute the multinomial coefficients, analyse its precision and performance. The other methods, analysed in our previous publ...

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Bibliographic Details
Published inNumerical algorithms Vol. 88; no. 2; pp. 837 - 851
Main Authors Araujo, Leonardo C., Sansão, João P. H., Vale-Cardoso, Adriano S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2021
Springer Nature B.V
Subjects
Algebra
Algorithms
Approximation
Binomial coefficients
Computer Science
Fourier transforms
Iterative methods
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Numerical analysis
Discrete Fourier transform
FFT
Multinomial coefficient
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ISSN1017-1398
1572-9265
DOI10.1007/s11075-020-01059-5

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Summary:In a previous publication, we have used the discrete Fourier transform to compute the binomial coefficients. In the present paper, we extend the previously proposed method to compute the multinomial coefficients, analyse its precision and performance. The other methods, analysed in our previous publication, are also extended to the multinomial case. The FFT method presents the best performance to compute all multinomial coefficients at a given level.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-01059-5