Matrix-valued radial basis functions: Stability estimates and applications

Advances in Computational Mathematics

Volumn 23, Issue 3, 2005, Pages 299-315

  Lowitzsch, Svenja ^a  

^a WEST VIRGINIA UNIVERSITY   (United States)

Author keywords

Divergence free; Incompressible; Interpolation; Matrix valued; Navier Stokes; Radial basis functions; Stability

Indexed keywords

EID: 33646742733     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-004-1786-8     Document Type: Article

References (12)

1. C. de Boor, A Practical Guide to Splines (Springer, New York, 1978).
2. J. Duchon, Splines minimizing rotation-invariant semi-norms in Sobolev spaces, in: Constructive Theory of Functions of Several Variables, eds. W. Schempp and K. Zeller (Springer, Berlin, 1977) pp. 85-100.
3. R.L. Hardy, Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res. 76 (1971) 1905-1915.
4. E.J. Kansa, Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics I. Surface approximations and partial derivative estimates, Comput. Math. Appl. 19 (1990) 127-145.
5. S. Lowitzsch, Interpolation and approximation employing divergence-free radial basis functions with applications, Ph.D. dissertation, Texas A&M University, College Station, TX, USA (2002).
6. S. Lowitzsch, Error estimates for matrix-valued radial basis function interpolation, J. Approx. Theory (2002) submitted.
7. F.J. Narcowich and J.D. Ward, Norms of inverses and condition numbers for matrices associated with scattered data, J. Approx. Theory 64 (1991) 69-94.
8. F.J. Narcowich and J.D. Ward, Norm estimates for the inverses of a general class of scattered-data radial-function interpolation matrices, J. Approx. Theory 69 (1992) 84-109.
9. F.J. Narcowich and J.D. Ward, Generalized Hermite interpolation via matrix-valued conditionally positive definite functions, Math. Comp. 63 (1994) 661-687.
10. R. Schaback, Error estimates and condition numbers for radial basis function interpolation, Adv. Comput. Math. 3 (1995) 251-264.
11. H. Wendland, Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree, Adv. Comput. Math. 4 (1995) 389-396.
12. H. Wendland, Error estimates for interpolation by compactly supported radial basis functions of minimal degree, J. Approx. Theory 93 (1998) 258-272.