Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
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Many multivariate interpolation schemes require as data values of derivatives that are not available in a practical application, and that therefore have to be generated suitably. A specific approach to this problem is described that is modeled after univariate spline interpolation. Derivative values are defined by the requirement that a certain functional be minimized over a suitable space subject to interpolation of given positional data. In principle, the technique can be applied in arbitrarily many variables. The theory is described in general, and a particular application is given in two variables. A major tool in the implementation of the technique is the Bezier-Bernstein form of a multivariate polynomial. The technique yields visually pleasing surfaces and is therefore suitable for design applications. It is less suitable for the approximation of derivatives of a given function.