Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-17T14:56:08.980Z Has data issue: false hasContentIssue false

On circulant matrices for certain periodic spline and histospline projections

Published online by Cambridge University Press:  17 April 2009

François Dubeau
Affiliation:
Départment de Mathématiques, Collège Militaire Royal de Saint-Jean, Saint-Jean-Sur-Richelieu, Quebec, JOJ IRO, Canada.
Jean Savoie
Affiliation:
Départment de Mathématiques, Collège Militaire Royal de Saint-Jean, Saint-Jean-Sur-Richelieu, Quebec, JOJ IRO, Canada.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present a unified treatment of the band circulant matrices which occur in the periodic spline and histospline projection theory with equispaced knots. Explicit bounds for the norm of these matrices are given.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Davis, P.J., Circulant matrices, (Wiley, New York 1979).Google Scholar
[2]Dubeau, F., “On band circulant matrices in the periodic spline interpolation theory”, Linear Algebra Appl. 72 (1985), 177182.CrossRefGoogle Scholar
[3]Dubeau, F. and Savoie, J., “Généralisation de la série géométrique et applications”, Ann. Sc. Math. Québec, (to appear).Google Scholar
[4]Kershaw, D., “A bound on the inverse of a band matrix which occurs in interpolation by periodic odd order splinesJ. Inst. Math. Appl. 20 (1977), 227228.CrossRefGoogle Scholar
[5]Lucas, T., “Asymptotic expansions for interpolating periodic splines”, SIAM J. Numer. Anal. 19 (1982), 10511066.CrossRefGoogle Scholar
[6]Micchelli, C.A., “Cardinal L-splines”, in Studies in Spline Functions and Approximation Theory, Karlin, Samuel, Micchelli, Charles A., Pinkus, Allan and Schoenberg, I.J. eds., (Academic Press, New York, 1976) 203250.Google Scholar
[7]ter Morsche, H., “On the relations between finite differences and derivatives of cardinal spline functions”, in Spline Functions, Böhmer, K., Meinardus, G. and Schempp, W., eds., (Berlin-Weidelberg-New YorkSpringer, 1976), 210219.CrossRefGoogle Scholar
[8]Schoenberg, I.J., Cardinal Spline Interpolation, CBMS Vol. 12 (Philadelphia, SIAM 1973).CrossRefGoogle Scholar
[9]Schoenberg, I.J., “On Micchelli's theorey of cardinal L-splines”, in Studies in Spline Functions and Approximation Theory, Karlin, Samuel, Micchelli, Charles A., Pinkus, Allan and Schoenberg, I.J., eds., (Academic Press, New York, 1976) 251276.Google Scholar