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<p><b>Abstract</b>—An algorithm for the linear interpolation of multi-input functions sampled on rectangular grids is presented. A geometric approach is adopted and the mathematics is thoroughly developed. We show that the algorithm is optimum. In fact, when the number <it>n</it> of inputs grows to infinity its computational requirement is <tmath>${\cal O}(n {\rm\ log}\ n),$</tmath> which is the same as the lower-bound on the cost of continuous linear interpolation procedures.</p>
Computational multidimensional geometry, high-speed function generation, piecewise-linear interpolation.

R. Rovatti, R. Guerrieri and M. Borgatti, "A Geometric Approach to Maximum-Speed n-Dimensional Continuous Linear Interpolation in Rectangular Grids," in IEEE Transactions on Computers, vol. 47, no. , pp. 894-899, 1998.
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