Linearly constrained reconstruction of functions by kernels with applications to machine learning

Advances in Computational Mathematics

Volumn 25, Issue 1-3, 2006, Pages 237-258

  Schaback, R ^a   Werner, J ^a  

^a NONE

Author keywords

Kernel machines; Machine learning; Positive definite radial basis functions; Quadratic programming; Regression; Support vector machines

Indexed keywords

EID: 33646752094     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-004-7616-1     Document Type: Article

References (18)

1. D. Braess, Chebyshev approximation by splines wuth free knots, Numer. Math. (1974) 357-366.
2. S. De Marchi, R. Schaback and H. Wendland, Optimal point locations for radial basis interpolation, in preparation (2002).
3. R. Fletcher, Practical Methods of Optimization (Wiley, 1987).
4. M. Frank and P. Wolfe, An algorithm for quadratic programming, Naval Res. Logist. Quart. 3 (1956) 95-110.
5. C.I. Barrodale and Phillips, Algorithm 495: Solution of an overdetermined system of linear equations in the Chebychev norm, ACM Trans. Math. Software (TOMS) 1 (1975) 264-270.
6. C.A. Micchelli, Interpolation of scattered data: Distance matrices and conditionally positive definite functions, Constr. Approx. 2 (1986) 11-22.
7. C.A. Micchelli and T.J. Rivlin, A survey of optimal recovery, in: Optimal Estimation in Approximation Theory, eds. C.A. Micchelli and T.J. Rivlin (Plenum Press, 1977) pp. 1-54.
8. C.A. Micchelli and T.J. Rivlin, Optimal recovery of best approximations, Results Math. 3 (1978) 25-32.
9. C.A. Micchelli and T.J. Rivlin, Lectures on optimal recovery, in: Numerical Analysis, Lancaster 1984, ed. P.R. Turner, Lecture Notes in Math. 1129 (Springer-Verlag, 1984) pp. 12-93.
10. C.A. Micchelli, T.J. Rivlin and S. Winograd, Optimal recovery of smooth function approximations, Numer. Math. 260 (1976) 191-200.
11. R. Schaback, Native Hilbert spaces for radial basis functions I, in: New Developments in Approximation Theory, eds. M.D. Buhmann, D.H. Mache, M. Felten and M.W. Müller, Internat. Ser. Numer. Math. 132 (Birkhäuser, 1999) pp. 255-282.
12. R. Schaback, Mathematical results concerning kernel techniques, Manuscript (2002).
13. R. Schaback and H. Wendland, Adaptive greedy techniques for approximate solution of large RBF systems, Numer. Algorithms 24 (2000) 239-254.
14. R. Schaback and H. Wendland, Numerical techniques based on radial basis functions, in: Curve and Surface Fitting, eds. A. Cohen, C. Rabut and L. Schumaker (Vanderbilt University Press, Nashville, TN, 2000).
15. B. Schölkopf and A.J. Smola, Learning with Kernels (MIT Press, 2002).
16. J. Stewart, Positive definite functions and generalizations, an historical survey, Rocky Mountain J. Math. 6 (1976) 409-434.
17. V. Vapnik, The Nature of Statistical Learning Theory (Springer, New York, 1995).
18. J. Werner, Optimization Theory and Applications (Vieweg, 1984).