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Numerical Evaluation of Special Functions
 In W. Gautschi (Ed.), AMS Proceedings of Symposia in Applied Mathematics 48
, 1994
"... . This document is an excerpt from the current hypertext version of an article that appeared in Walter Gautschi (ed.), Mathematics of Computation 19431993: A HalfCentury of Computational Mathematics, Proceedings of Symposia in Applied Mathematics 48, American Mathematical Society, Providence, ..."
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. This document is an excerpt from the current hypertext version of an article that appeared in Walter Gautschi (ed.), Mathematics of Computation 19431993: A HalfCentury of Computational Mathematics, Proceedings of Symposia in Applied Mathematics 48, American Mathematical Society, Providence, RI 02940, 1994. The symposium was held at the University of British Columbia August 913, 1993, in honor of the fiftieth anniversary of the journal Mathematics of Computation. The original abstract follows. Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field. 5.9. Mathieu, Lam'e, and Spheroidal Wave Functions. 5.9.1. Characteristic Values of Mathieu's Equation. Software Packages:...
UNRESTRICTED ALGORITHMS FOR ELEMENTARY AND SPECIAL FUNCTIONS
"... We describe some “unrestricted” algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by examples. Applications of such algorithms are mentioned. ..."
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We describe some “unrestricted” algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by examples. Applications of such algorithms are mentioned.
Parametric versus Nonparametric Estimation of Diffusion Processes – A Monte Carlo Comparison. Working Paper
 Journal of Finance. Forthcoming
, 1997
"... In this paper, a Monte Carlo simulation is performed to investigate the finite sample properties of various estimators, based on discretely sampled observations, of the continuoustime Itô diffusion process. The simulation study aims to compare the performance of the nonparametric estimators propose ..."
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In this paper, a Monte Carlo simulation is performed to investigate the finite sample properties of various estimators, based on discretely sampled observations, of the continuoustime Itô diffusion process. The simulation study aims to compare the performance of the nonparametric estimators proposed in Jiang and Knight (1996) with common parametric estimators based on those diffusion processes which have explicit transition density functions. The simulation results show that, with a large sample over a short sampling period, although all the parametric diffusion estimators perform very well, the parametric drift estimators perform very poorly. However, both the nonparametric diffusion and drift estimators perform reasonably well.
Guaranteed Precision for Transcendental and Algebraic Computation made Easy
, 2006
"... Dedicated to the friends and families who blessed and supported me iv ..."
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Dedicated to the friends and families who blessed and supported me iv
Symbolic and Numerical Computation on Bessel Functions of Complex Argument and Large Magnitude
, 1996
"... The Lanczos ømethod, with perturbations proportional to Faber polynomials, is employed to approximate the Bessel functions of the first kind J (z) and the second kind Y (z), the Hankel functions of the first kind H (1) (z) and the second kind H (2) (z) of integer order for specific ..."
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The Lanczos ømethod, with perturbations proportional to Faber polynomials, is employed to approximate the Bessel functions of the first kind J (z) and the second kind Y (z), the Hankel functions of the first kind H (1) (z) and the second kind H (2) (z) of integer order for specific outer regions of the complex plane, i.e. jzj R for some R. The scaled symbolic representation of the Faber polynomials and the appropriate automated ømethod approximation are introduced. Both symbolic and numerical computation are discussed. In addition, numerical experiments are employed to test the proposed ømethod. Computed accuracy for J 0 (z) and Y 0 (z) for jzj 8 are presented. The results are compared with those obtained from the truncated Chebyshev series approximations and with those of the ø  method approximations on the inner disk jzj 8. Some concluding remarks and suggestions on future research are given. Key words and phrases. Automated ømethod, symbolic Faber polynomi...