Abstract
In this chapter, we construct rational approximations of PSWFs. More specifically, we approximate the reciprocal of ψ n in the interval ( −1,1) by a rational function having n poles (these poles happen to be precisely the n roots of ψ n in (−1,1)). Also, we derive explicit bounds on the error of such approximations. The underlying analysis is based on a detailed investigation of certain properties of PSWFs outside the interval (−1,1) (see also [49, 50]).
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Bibliography
A. Osipov, V. Rokhlin, Detailed analysis of prolate quadratures and interpolation formulas, Yale CS Technical Report #1458, 2012.
A. Osipov, V. Rokhlin, Detailed analysis of prolate quadratures and interpolation formulas, arXiv:1208.4816v1, 2012.
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Osipov, A., Rokhlin, V., Xiao, H. (2013). Rational Approximations of PSWFs. In: Prolate Spheroidal Wave Functions of Order Zero. Applied Mathematical Sciences, vol 187. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-8259-8_6
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DOI: https://doi.org/10.1007/978-1-4614-8259-8_6
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