The stable evaluation of multivariate simplex splines

Author:
Thomas A. Grandine

Journal:
Math. Comp. **50** (1988), 197-205

MSC:
Primary 65D07; Secondary 41A15, 41A63

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917827-2

MathSciNet review:
917827

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper gives a general method for the stable evaluation of multivariate simplex splines, based on the well-known recurrence relation of Micchelli [12]. This paper deals with two problems which arise in the implementation of the recurrence relation. First, the coefficients in the recurrence are shown to be efficiently computable via the dual simplex method of linear programminig. Secondly, the problem of evaluation along mesh boundaries is discussed in detail.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917827-2

Keywords:
*B*-spline,
simplex spline,
multivariate,
recurrence relation,
linear programming,
simplex method

Article copyright:
© Copyright 1988
American Mathematical Society