Abstract
We present an algorithm for the computation of interpolatory splines of arbitrary order at triadic rational points. The algorithm is based on triadic subdivision of splines. Explicit expressions for the subdivision symbols are established. These are rational functions. The computations are implemented by recursive filtering.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Schoenberg, I.J.: Contribution to the problem of approximation of equidistant data by analytic functions. Quart. Appl. Math. 4, 45–99, 112–141 (1946)
Schoenberg, I.J.: Cardinal interpolation and spline functions. J. Approx. Theory 2, 167–206 (1969)
Schoenberg, I.J.: Cardinal interpolation and spline functions II. J. Approx. Theory 6, 404–420 (1972)
Schoenberg, I.J.: Cardinal Spline Interpolation. CBMS, vol. 12. SIAM, Philadelphia (1973)
Zheludev, V.A.: Integral representation of slowly growing equidistant splines. Approx. Theory Appl. 14(4), 66–88 (1998)
Zheludev, V.A.: Interpolatory subdivision schemes with infinite masks originated from splines. Adv. Comput. Math. 25, 475–506 (2006)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Tim Goodman.
Rights and permissions
About this article
Cite this article
Zheludev, V.A., Averbuch, A.Z. Computation of interpolatory splines via triadic subdivision. Adv Comput Math 32, 63 (2010). https://doi.org/10.1007/s10444-008-9087-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10444-008-9087-2