Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T08:26:01.105Z Has data issue: false hasContentIssue false
  • English
  • Français

Application of Reproducing Kernel Hilbert Spaces to a Minimization Problem with Prescribed Nodes

Published online by Cambridge University Press:  28 May 2015

Hendra Gunawan  and
Yoshihiro Sawano
Hendra Gunawan*
Affiliation:
Department of Mathematics, Institut Teknologi Bandung, Bandung, Indonesia
Yoshihiro Sawano
Affiliation:
Department of Mathematics, Kyoto University, Kyoto, Japan
*
Corresponding author. Email: hgunawan@math.itb.ac.id
Get access

Abstract

The theory of reproducing kernel Hilbert spaces is applied to a minimization problem with prescribed nodes. We re-prove and generalize some results previously obtained by Gunawan et al. [2,3], and also discuss the Hölder continuity of the solution to the problem.

Keywords

41A5042A1042A1565T4074G65Reproducing kernel Hilbert spacesminimization problemnodes
Type
Review Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 4 , November 2011 , pp. 372 - 378
Copyright
Copyright © Global-Science Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ambarwati, L. and Gunawan, H., “On the product of Chebyshev systems”, submitted for publication.Google Scholar
[2]Gunawan, H., Pranolo, F. and Rusyaman, E., “An interpolation method that minimizes an energy integral of fractional order”, in Kapur, D. (ed.), ASCM 2007, LNAI 5081 (2008), 151–162.Google Scholar
[3]Gunawan, H., Rusyaman, E. and Ambarwati, L., “Surfaces with prescribed nodes and minimum energy integral of fractional order”, to appear in ITB J. Sci. (2011).Google Scholar
[4]Lorentz, G. G., Approximation of Functions, AMS Chelsea Publishing, Providence, 1966.Google Scholar
[5]Schölkopf, B. and Smola, A. J., Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT Press, Cambridge, 2002.Google Scholar
[6]Sugimoto, M. and Tomita, N., “The dilation property of modulation spaces and their inclusion relation with Besov spaces”, J. Funct. Anal. 248 (2007), 79–106.Google Scholar
[7]Taibleson, M. H., “On the theory of Lipschitz spaces of distributions on Euclidean n-space. I. Principal properties”, J. Math. Mech. 13 (1964), 407–479.Google Scholar