An interpolation method taking into account inequality constraints: I. Methodology |
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| Authors: | Olivier Dubrule and Clement Kostov |
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| Institution: | (1) 1 Lincoln Center, Sohio Petroleum Company, 5400 LBJ Freeway, Suite 1200, 75240 Dallas, Texas;(2) Department of Applied Earth Sciences, Stanford University, 94305 Stanford, California |
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| Abstract: | Several kinds of data can provide information about a variable measured on a one- or two-dimensional space; at some points, the value is known to be equal to a certain number. At other points, the only information may be that the variable is greater or smaller than a given value. The theory of splines provides interpolating functions that can take into account both equality and inequality data. These interpolating functions are presented. The parallel between splines and kriging is reviewed, using the formalism of dual kriging. Coefficients of dual kriging can be obtained directly by minimizing a quadratic form. By adding some inequality constraints to this minimization, an interpolating function may be calculated which takes into account inequality data and is more general than a spline. The method is illustrated by some simple one-dimensional examples.Work performed at Sohio Petroleum Company |
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| Keywords: | kriging splines mapping prediction |
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