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Cubic Splines with Infinite Derivatives at Some Knots

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1 Author(s)
Inselberg, A. ; IBM Data Processing Division Scientific Center, 1930 Century Park West, Los Angeles, California 90067, USA

A generalization of cubic spline interpolation with vertical slopes at some knots is proposed. An existence theorem including an algorithm for constructing such generalized splines is proved. The resulting splines are obtained in closed form and they are partition invariant.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:20 ,  Issue: 5 )