Algorithms and codes for the Macdonald function: recent progress and comparisons

Authors:
B. R. Fabijonas;D. W. Lozier;J. M. Rappoport
Affiliations:
Department of Mathematics, Southern Methodist University, PO Box 750156, Dallas, TX;Information Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, MD;Russian Academy of Sciences, Vlasov Street, Building 27, Apt. 8, Moscow, 117335, Russian Federation
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

The modified Bessel function Kiv(x), also known as the Macdonald function, finds application in the Kontorovich-Lebedev integral transform when x and v are real and positive. In this paper, a comparison of three codes for computing this function is made. These codes differ in algorithmic approach, timing, and regions of validity. One of them can be tested independent of the other two through Wronskian checks, and therefore is used as a standard against which the others are compared.