C1 surface interpolation with constraints
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Givenn pairwise distinct and arbitrarily spaced pointsPi in a domainD of thex−y plane andn real numbersfi, consider the problem of computing a bivariate functionf(x, y) of classC1 inD whose values inPi are exactlyfi,i=1,…,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQl inD.
In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.
The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.
KeywordsBivariate interpolation quadratic programming method of multipliers parallel computation
AMS subject classification65D05 65K05
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