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An algorithm for constructing a basis for $C^{r}$-spline modules over polynomial rings


Authors: Satya Deo and Lipika Mazumdar
Journal: Math. Comp. 67 (1998), 1107-1120
MSC (1991): Primary 41A15; Secondary 13C10
DOI: https://doi.org/10.1090/S0025-5718-98-00943-0
MathSciNet review: 1459386
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Abstract: Let $\Box$ be a polyhedral complex embedded in the euclidean space $E^{d}$ and $S^{r}(\Box)$, $r \geq 0$, denote the set of all $C^{r}$-splines on $\Box$. Then $S^{r}(\Box)$ is an $R$-module where $R = E[x_{1},\ldots,x_{d}]$ is the ring of polynomials in several variables. In this paper we state and prove the existence of an algorithm to write down a free basis for the above $R$-module in terms of obvious linear forms defining common faces of members of $\Box$. This is done for the case when $\Box$ consists of a finite number of parallelopipeds properly joined amongst themselves along the above linear forms.


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Additional Information

Satya Deo
Affiliation: Department of Mathematics and Computer Science, R.D. University, Jabalpur - 482 001, India
Email: sdt@rdunijb.ren.nic.in

Lipika Mazumdar
Affiliation: Department of Mathematics and Computer Science, R.D. University, Jabalpur - 482 001, India

DOI: https://doi.org/10.1090/S0025-5718-98-00943-0
Received by editor(s): December 15, 1994
Received by editor(s) in revised form: March 3, 1997
Additional Notes: The first author was supported by the UGC research project no. F 8-5/94 (SR-I)
The second author was supported by the CSIR(JRF) no. 9/97(36)/92/EMR-I
Article copyright: © Copyright 1998 American Mathematical Society

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