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An Application of the Finite Element Approximation Method to Find the Complex Zeros of the Modified Bessel Function $K_n(z)$
K. V. Leung and S. S. Ghaderpanah
Mathematics of Computation
Vol. 33, No. 148 (Oct., 1979), pp. 1299-1306
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2006465
Page Count: 8
You can always find the topics here!Topics: Approximation, Zero, Bessel functions, Modified Bessel functions, Mathematical functions, Finite element method, Personnel evaluation, Coordinate systems, Algorithms
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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.
Mathematics of Computation © 1979 American Mathematical Society