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Some properties of periodic B-spline collocation matrices

Published online by Cambridge University Press:  14 November 2011

S. L. Lee ,
C. A. Micchelli ,
A. Sharma  and
P. W. Smith
S. L. Lee
Affiliation:
University of Malaysia, Penang, Malaysia
C. A. Micchelli
Affiliation:
IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, U.S.A
A. Sharma
Affiliation:
University of Alberta, Edmonton, Canada
P. W. Smith
Affiliation:
Old Dominion University, Norfolk, Virginia, U.S.A
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Synopsis

In three recent papers by Cavaretta et al., progress has been made in understanding the structure of bi-infinite totally positive matrices which have a block Toeplitz structure. The motivation for these papers came from certain problems of infinite spline interpolation where total positivity played an important role.

In this paper, we re-examine a class of infinite spline interpolation problems. We derive new results concerning the associated infinite matrices (periodic B-spline collocation matrices) which go beyond consequences of the general theory. Among other things, we identify the dimension of the null space of these matrices as the width of the largest band of strictly positive elements.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 3-4 , 1983 , pp. 235 - 246
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

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