Gamma Solution - Warren, James R

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Résumé :
The Gamma Function is a generalisation of the factorial for use with complex numbers. The plane of complex numbers subsumes fractions including transcendental numbers, some of which have especially elegant Gamma forms. The Gamma Function has a number of applications in advanced science including quantum physics, astrophysics and fluid dynamics An analytical and experimental study was undertaken to assess how theoretical and experimental code and performance metrics might assist the choice of published Complete Gamma Function ( CGF ) solution algorithms, or inform the development of new CGF methods. Accuracy, speed and component timing statistics were computed for thirteen methods or method variations, and new empirical metrics proposed. Empirical metrics and component time profiles disclosed significant algorithm properties and assisted coding optimisations. Halstead metrics did not apply, but code token ratios correlated with other CGF algorithm features. Further research could involve recently discovered Elliptic, Laplacian or Zeta Function avenues. Enjoy the work and I hope you find it useful as a starting point. Extensive equations and diagrams are included, as well as program code in Visual Basic...

Biographie:
James R Warren was born in Cumberland, England in 1952.Educated at Ware Secondary Modern School and the Aberdeen College of Commerce, Dr Warren is a graduate of Manchester, Strathclyde and Birmingham City Universities and was for twenty years a Senior Lecturer in Information Technology and Quantitative Methods.James Warren is a former Fellow of the Geological Society of London, and a past Member of The Institution of Water Engineers and Scientists, the Institute of Electrical and Electronic Engineers and the Association for Computing Machinery.James lives with his wife Jana in Bloxwich, England.

Sommaire:
The Gamma Function is a generalisation of the factorial for use with complex numbers. The plane of complex numbers subsumes fractions including transcendental numbers, some of which have especially elegant Gamma forms. The Gamma Function has a number of applications in advanced science including quantum physics, astrophysics and fluid dynamics An analytical and experimental study was undertaken to assess how theoretical and experimental code and performance metrics might assist the choice of published Complete Gamma Function ( CGF ) solution algorithms, or inform the development of new CGF methods. Accuracy, speed and component timing statistics were computed for thirteen methods or method variations, and new empirical metrics proposed. Empirical metrics and component time profiles disclosed significant algorithm properties and assisted coding optimisations. Halstead metrics did not apply, but code token ratios correlated with other CGF algorithm features. Further research could involve recently discovered Elliptic, Laplacian or Zeta Function avenues. Enjoy the work and I hope you find it useful as a starting point. Extensive equations and diagrams are included, as well as program code in Visual Basic...