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Norm estimates of interpolation matrices and their inverses associated with strictly positive definite functions
Author(s):
J.
Levesley;
Z.
Luo;
X.
Sun
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2127-2134.
MSC (1991):
Primary 65F35
Posted:
February 26, 1999
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Abstract:
In this paper, we estimate the norms of the interpolation matrices and their inverses that arise from scattered data interpolation on spheres with strictly positive definite functions.
References:
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- Lebedev, N.N., Special Functions and their Applications, Prentice Hall, Englewood Cliffs, NJ, 1965. MR 30:4988
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- Müller, C., Spherical Harmonics, Lecture Notes in Mathematics, vol. 17, Springer-Verlag, Berlin, Heidelberg, New York, 1966. MR 33:7593
- [NW1]
- Narcowich, F.J. and Ward, J.D., Norms of inverses and condition numbers for matrices associated with scattered data, J. Approx. Theory 64 (1991), 69-94. MR 92b:65017
- [NW2]
- Narcowich, F.J. and Ward, J.D., Norm estimates for inverses of a general class of scattered data radial function interpolation matrices, J. Approx. Theory 69 (1992), 84-109.
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- Ron A. and Sun, X., Strictly positive definite functions on spheres, Mathematics of Computation 65 (1996), 1513-1530. MR 97a:41032
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- Schreiner, M., Locally supported kernels for spherical spline interpolation, J. Approx. Theory (to appear). CMP 97:12
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Additional Information:
J.
Levesley
Affiliation:
Department of Mathematics and Computer Sciences, University of Leicester, Leicester LE1 7RH, England
Email:
jl1@mcs.le.ac.uk
Z.
Luo
Affiliation:
Department of Mathematics and Computer Sciences, University of Leicester, Leicester LE1 7RH, England
Email:
zl3@mcs.le.ac.uk
X.
Sun
Affiliation:
Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712
Address at time of publication:
Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
Email:
xis280f@cnas.smsu.edu
DOI:
10.1090/S0002-9939-99-04683-3
PII:
S 0002-9939(99)04683-3
Received by editor(s):
December 26, 1996
Received by editor(s) in revised form:
August 26, 1997
Posted:
February 26, 1999
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1999,
American Mathematical Society
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