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Riesz Bases of Splines and Regularized Splines with Multiple Knots

✍ Scribed by K. Jetter; J. Stöckler

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
925 KB
Volume
87
Category
Article
ISSN
0021-9045

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✦ Synopsis

This paper deals with L 2 (R)-norm and Sobolev-norm stability of polynomial splines with multiple knots, and with regularized versions thereof. An essential ingredient is a result on Ho lder continuity of the shift operator operating on a B-spline series. The stability estimates can be reformulated in terms of a Riesz basis property for the underlying spline spaces. These can also be employed to derive a result on stable Hermite interpolation on the real line. We point to the connection with the problem of symmetric preconditioning of bi-infinite interpolation matrices.

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