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Bounded property and point control of a bivariate rational interpolating surface. (English) Zbl 1141.65013

The authors consider a certain smooth interpolant \(f(x,y)\) of real-valued data \(f_{i,j}\) located at sites \((x_i,y_j)\), with \(x_1<\cdots<x_n\) and \(y_1<\cdots<y_m\), which also interpolates discrete differences in the \(x\) and \(y\) direction, and which has been previously constructed by partly the same authors [Appl. Math. Comput. 168, No. 2, 990-1003 (2005; Zbl 1081.41002)]. It is shown that the values of \(f(x,y)| _{[x_i,x_{i+1}]\times[y_i,y_{i+1}]}\) are bounded by \({9\over 4}\max_{r,s\in\{0,1,2\}} | f_{i+r,j+s}| \). Further it is discussed how to tune parameters in the construction of the interpolant to achieve certain properties.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D05 Numerical interpolation
65D07 Numerical computation using splines

Citations:

Zbl 1081.41002
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References:

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