Optimal Multivariate Interpolation

Mathematics in Industry

Volumn 7, Issue , 2005, Pages 389-407

  Werther, Tobias ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Interpolation Problem; Linear Unbiased Prediction; Optimal Interpolation; Relative Absolute Error; Thin Plate Spline

Indexed keywords

EID: 39449134569     PISSN: 16123956     EISSN: 21983283     Source Type: Book Series    
DOI: 10.1007/3-540-26493-0_12     Document Type: Chapter

References (16)

1. J.H. Ahlberg, E.N. Nilson, and J.L. Walsh (1967) The Theory of Splines and Their Applications. Academic Press, New York.
2. I.C. Briggs (1974) Machine contouring using minimum curvature. Geophysics 39(1), 39–48.
3. P.G. Ciarlet (1978) The Finite Element Method for Elliptic Problems. SIAM Classics in Applied Mathematics.
4. N.A.C. Cressie (1991) Statistics for Spatial Data. John Wiley.
5. R. Fletcher (1987) Practical Methods in Optimization. 2nd edition, John Wiley and Sons.
6. A. Iske (2002) Scattered data modelling using radial basis functions. Tutorials on Multiresolution in Geometric Modelling, A. Iske, E. Quak, and M. S. Floater (eds.), Springer, Heidelberg, 205–242.
7. P.K. Kitanidis (1986) Parameter uncertainty in estimation of spatial functions: Bayesian analysis. Water Resource Research 19, 499–507.
8. G. Matheron (1981) Splines and kriging: their formal equivalence. Down-to-Earth Statistics: Solutions Looking for Geological Problems, D.F. Merriam (ed.), Syracuse University Geology Contributions, 77–95.
9. C.A. Micchelli (1986) Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constr. Approx. 2, 11–22.
10. H. Omre (1987) Bayesian kriging-merging observations and qualified guesses in kriging. Math. Geol. 19, 25–39.
11. W. Rudin (1991) Functional Analysis. 2nd edition, Mc Graw-Hill.
12. L. Schwartz (1966) Théorie des Distributions. Hermann, Paris.
13. M.L. Stein (1999) Interpolation of Spatial Data. Springer.
14. T. Werther (2003) Characterization of semi-Hilbert spaces with application in scattered data interpolation. Curve and Surface Fitting: Saint-Malo 2002, A. Cohen, J.-L. Merrien, and L.L. Schumaker (eds.), Nashboro Press, Brent-wood, 374–383.
15. T. Werther (2003) Optimal Interpolation in Semi-Hilbert Spaces. PhD thesis, University of Vienna.
16. F. Ziegler (1998) Technische Mechanik der festen und flüssigen Körper. Springer.