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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An application of the finite element approximation method to find the complex zeros of the modified Bessel function $ K\sb{n}(z)$


Authors: K. V. Leung and S. S. Ghaderpanah
Journal: Math. Comp. 33 (1979), 1299-1306
MSC: Primary 65D20; Secondary 33-04
MathSciNet review: 537975
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Abstract: Using a finite element approximation, an iterative optimization scheme is described to find the z zeros of $ {K_n}(z)$ for fixed order n. Two computer programs have been implemented to find the complex zeros with a computational accuracy of either 13 or 27 significant digits. The optimization scheme described in the paper may also be readily applied to find real and complex zeros of an arbitrary function with real and complex coefficients. Neither its accuracy nor its efficiency is affected by the number of the roots of the function.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1979-0537975-3
PII: S 0025-5718(1979)0537975-3
Keywords: Bessel functions, complex zeros, finite element approximation
Article copyright: © Copyright 1979 American Mathematical Society