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We show how a newly developed multivariate data fitting technique and its extensions enables to solve a variety of scientific computing problems in: signal processing, mathematical finance and computer graphics. We capture linear as well as nonlinear phenomena because a generalized multivariate rational model is used.

The technique is a refinement of the basic ideas developed and interpolates interval data. Intervals allow to take the inherent data error in measurements and simulation into consideration, whilst guaranteeing an upper bound on the tolerated range of uncertainty. The latter is the main difference with a least squares technique which does as well as it can, but without respecting an imposed threshold on the approximation error. In applications where industry standards and shape conditions (positivity, monotonicity, convexity) need to be guaranteed, the interval interpolation technique may be a valuable alternative.