Staircase Algorithm and Boundary Valued Convex Interpolation by Gregory’s Splines
In 1984, the staircase algorithm was introduced as an abstract concept for solving weakly coupled systems of inequalities. Originally this algorithm was described by means of projections of relations. Recently a composition based form was proposed allowing further applications. Now, using this new proposal we derive a concrete algorithm for the problem of boundary valued convex interpolation applying Gregory’s rational cubic splines. It turns out that these splines always guarantee success under natural compatibility conditions.
KeywordsRationality Parameter Spline Interpolation Strict Convexity Convex Position Convexity Relation
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