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Given a bivariate data set, how does one obtain the most accurate least-squares polynomial approximation under the constraint that the resulting polynomial is non-decreasing. Similarly, how does one proceed with a trivariate data set with the same constraint applying to the resulting bivariate polynomial.

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    $\begingroup$ Is it a Mathematica question? Looks like it is a general mathematical problem. Can you provide an example of such data and indicate why least square fit is unsatisfactory. $\endgroup$
    – yarchik
    Jun 28 at 9:38
  • $\begingroup$ Yet another point, the polynomial should be non-descreasing in what direction? $\endgroup$
    – yarchik
    Jun 28 at 9:40

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