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Tangent Space Methods for Approximation on Compact Homogeneous Manifolds

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Book cover Recent Progress in Multivariate Approximation

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 137))

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Abstract

Tangent space ideas are utilised to prove convergence of invariant kernel interpolation on compact homogeneous manifolds, as well as Taylor series type estimates for polynomial approximation on the same manifolds.

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References

  1. L. Bos, S. de Marchi: Limiting values under scaling of the Lebesgue function for polynomial interpolation on spheres, J. Approx. Theory 96 (1999), 366–377.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Duchon: Sur l’erreur d’interpolation des fonctions de plusieurs variables par les D m -splines, RAIRO Anal. Num. 12 (1978), 325–334.

    MathSciNet  MATH  Google Scholar 

  3. M. Golomb, H. F. Weinberger: Optimal approximation and error bounds, in: R. E. Langer (Ed): On Numerical Approximation, Univ. Wisconsin Press, Madison 1959, pp. 117–190.

    Google Scholar 

  4. M. von Golitschek, W. A. Light: Interpolation by polynomials and radial basis functions on spheres, Constr. Approx. 17 (2001), 1–18.

    Article  MathSciNet  MATH  Google Scholar 

  5. K. Jetter, J. Stöckier, J. D. Ward: Error estimates for scattered data interpolation on spheres, Math. Comp. 68 (1999), 733–747.

    Article  MathSciNet  MATH  Google Scholar 

  6. W. R. Madych, S. A. Nelson: Multivariate interpolation and conditionally positive definite functions II, Math. Comp. 54 (1990), 211–230.

    Article  MathSciNet  MATH  Google Scholar 

  7. L. L. Schumaker, T. Lyche: A multiresolution tensor spline method for fitting functions on the sphere, SIAM J. Sci. Comput. 22 (2000), 724–746.

    Article  MathSciNet  MATH  Google Scholar 

  8. G. Wahba: Spline interpolation and smoothing on the sphere,SIAM J. Sci. Statist. Comput. 2 (1981), 5–16, and 3 (1982), 385–386.

    Google Scholar 

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© 2001 Springer Basel AG

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Levesley, J. (2001). Tangent Space Methods for Approximation on Compact Homogeneous Manifolds. In: Haussmann, W., Jetter, K., Reimer, M. (eds) Recent Progress in Multivariate Approximation. ISNM International Series of Numerical Mathematics, vol 137. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8272-9_16

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  • DOI: https://doi.org/10.1007/978-3-0348-8272-9_16

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9498-2

  • Online ISBN: 978-3-0348-8272-9

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