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Prolate Spheroidal Wave Functions of Order Zero

Part of the book series: Applied Mathematical Sciences ((AMS,volume 187))

Abstract

In this chapter, we present an overview of the results from the rest of this book. Throughout this chapter, the real number c > 0 will be the band limit, and the natural number n ≥ 0 will be the index of the nth prolate spheroidal wave function (PSWF).

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Bibliography

  1. H. Cheng, N. Yarvin, V. Rokhlin, Non-linear Optimization, Quadrature and Interpolation, SIAM J. Optim. 9, 901–23, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. Dahlquist, A. Björk, Numerical Methods, Prentice-Hall Inc., 1974.

    Google Scholar 

  3. W. H. J. Fuchs, On the eigenvalues of an integral equation arising in the theory of band-limited signals, J. Math. Anal. Appl. 9 317–330 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Golub, C. V. Loan, Matrix Computations, Second Edition, Johns Hopkins University Press, Baltimore, 1989.

    MATH  Google Scholar 

  5. J. Ma, V. Rokhlin, S. Wandzura, Generalized Gaussian Quadratures for Systems of Arbitrary Functions, SIAM J. Numer. Anal. 33, 971–96, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  6. A. Osipov, Evaluation of small elements of the eigenvectors of certain symmetric tridiagonal matrices with high relative accuracy, Yale CS Technical Report #1460, 2012.

    Google Scholar 

  7. A. Osipov, Evaluation of small elements of the eigenvectors of certain symmetric tridiagonal matrices with high relative accuracy, arXiv:1208.4906v1, 2012.

    Google Scholar 

  8. W. Rudin, Real and Complex Analysis, Mc-Graw Hill Inc., 1970.

    Google Scholar 

  9. N. Yarvin, V. Rokhlin, Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators, SIAM J. Sci. Comput. 20, 699–718, 1998.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Yale University, New Haven, CT, USA

    Andrei Osipov

  2. Department of Computer Science, Yale University, New Haven, CT, USA

    Vladimir Rokhlin

  3. Department of Computer Science, University of California, Davis, CA, USA

    Hong Xiao

Authors
  1. Andrei Osipov
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  2. Vladimir Rokhlin
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  3. Hong Xiao
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Osipov, A., Rokhlin, V., Xiao, H. (2013). Overview. 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_3

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