POSITIVE THIN PLATE SPLINES

<正> We consider the problem of interpolating positive data at scat-tered data points of the plane R2. To solve the problem, weintroduce the Positive Thin Plate Spline, i. e. the solution to Minimize integral from n=R2{x2/2u}2 + 2{xy/2u}2 + {y2/2u}2, u ∈ D-2L2（R2）; u（tj） = zj, j=1…, n; u（t）≥0, t∈ Kwhere （tj, zj） are the data, K is a convex compact subset of R2.We give existence, uniqueness, characterisation and convergenceresults. We also present a dual algorithm to compute this splineand show numerical experience with the method.