Abstract
In this chapter, we describe several classes of prolate spheroidal wave function (PSWF)-based quadrature rules and interpolation formulas, designed for band-limited functions with a specified band limit c > 0 over the interval [ − 1, 1] (see also [49, 50, 53–55, 73]).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsBibliography
M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover Publications, 1964.
W. E. Boyce, R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Seventh Edition, John Wiley and Sons, Inc., 2001.
H. Cheng, N. Yarvin, V. Rokhlin, Non-linear Optimization, Quadrature and Interpolation, SIAM J. Optim. 9, 901–23, 1999.
E. Isaacson, H. B. Keller, Analysis of Numerical Methods, New York: Wiley, 1966.
J. Ma, V. Rokhlin, S. Wandzura, Generalized Gaussian Quadratures for Systems of Arbitrary Functions, SIAM J. Numer. Anal. 33, 971–96, 1996.
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.
A. Osipov, V. Rokhlin, On the evaluation of prolate spheroidal wave functions and associated quadrature rules, Appl. Comput. Harmon. Anal. (2013), http://dx.doi.org/10.1016/j.acha.2013.04.002.
A. Osipov, V. Rokhlin, On the evaluation of prolate spheroidal wave functions and associated quadrature rules, arXiv:1301.1707v1, 2013.
W. Rudin, Real and Complex Analysis, Mc-Graw Hill Inc., 1970.
J. Stoer and R. Bulirsch, Introduction To Numerical Analysis, 2’nd ed., Springer-Verlag, 1992.
H. Xiao, V. Rokhlin, N. Yarvin, Prolate spheroidal wavefunctions, quadrature and interpolation, Inverse Problems, 17(4):805–828, 2001.
N. Yarvin, V. Rokhlin, Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators, SIAM J. Sci. Comput. 20, 699–718, 1998.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Osipov, A., Rokhlin, V., Xiao, H. (2013). Quadrature Rules and Interpolation via 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_9
Download citation
DOI: https://doi.org/10.1007/978-1-4614-8259-8_9
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-8258-1
Online ISBN: 978-1-4614-8259-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)