The following information was submitted:
Transactions: WSEAS TRANSACTIONS ON ADVANCES IN ENGINEERING EDUCATION
Transactions ID Number: 89-124
Full Name: Gianfranco Chicco
Position: Associate Professor
Age: ON
Sex: Male
Address: Dipartimento di Ingegneria Elettrica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino
Country: ITALY
Tel: 011 090 7141
Tel prefix: +39
Fax: +39 011 090 7199
E-mail address: gianfranco.chicco@polito.it
Other E-mails: gianfranco.chicco@yahoo.com
Title of the Paper: A novel continuous function for approximation to the factorial
Authors as they appear in the Paper: Gianfranco Chicco
Email addresses of all the authors: gianfranco.chicco@polito.it
Number of paper pages: 11
Abstract: Various approximations to the factorial have been proposed in the literature to formulate continuous functions in which the argument is a non-negative variable. Most of these approximations are based on the classical De-Moivre-Stirling's or shortly Stirling's formula. Further approximations have been provided, either multiplying the Stirling's formula to a correction function, or introducing some structural modifications to the Stirling's formula. The characteristics of the various approximations can be pointed out by investigating how the correction function or the structurally modified formula can provide a better representation of the factorial for natural numbers with respect to the classical Stirling's formula. This paper starts with a tutorial illustration of the characteristics of various approximations to the factorial, and contains the proposal of a novel continuous function with relatively simple structure. The proposed function has very low relative appr!
oximation errors with respect to the factorial; furthermore, the relative approximation error is always positive. These characteristics enable the novel function to be used as an upper bound to the factorial. Application examples of the proposed formula in the pattern recognition domain are presented, in order to obtain factorial-free formulations for the calculation of orthogonal Fourier-Mellin moments and Pseudo-Zernike moments, with some notes on the possible computational complexity reduction obtainable by exploiting the proposed formulation with respect to the computation of the same moments using the factorials, in analogy to what has been done in the literature by using a different type of approximation.
Keywords: Factorial, Stirling's formula, Asymptotic convergence, Correction function, Relative approximation error, Orthogonal Fourier-Mellin moments, Pseudo-Zernike moments.
EXTENSION of the file: .pdf
Special (Invited) Session: On approximations to the factorial
Organizer of the Session: 626-401
How Did you learn about congress:
IP ADDRESS: 109.115.66.203
