| 摘 要： | We consider the problem of interpolating positive data at scat-tered data points of the plane R~2. To solve the problem, weintroduce the Positive Thin Plate Spline, i. e. the solution to Minimize integral from n=R~2{x~2/~2u}~2 + 2{xy/~2u}~2 + {y~2/~2u}~2, u ∈ D~(-2)L~2(R~2); u(t_j) = z_j, j=1…, n; u(t)≥0, t∈ Kwhere (t_j, z_j) are the data, K is a convex compact subset of R~2.We give existence, uniqueness, characterisation and convergenceresults. We also present a dual algorithm to compute this splineand show numerical experience with the method.
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