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# Fitting by least squares

As is often the case, a contour plot may not be judged so much for its accuracy as for its neatness. For example, critical points could be expected to be relatively rare and so it might be thought that the crudeness of the linear approximation in the vicinity of a critical point would go unnoticed. However, exactly the opposite is true, to the extent that contour maps are often prepared for the sole purpose of locating the critical points, leaving the remainder of the diagram as the part likely to be ignored.

It is also true that a least squares fitting of a linear or quadratic approximation obtained by combining the data points of several simplices may sometimes be preferred to the more detailed representation derived from the individual simplices. It is then necessary to construct the normal equations from the data, and invert their coefficient matrix, to obtain the parameters to represent the contour, with the added complication of having to join the contours smoothly as they pass from one region to another. Moreover, the coefficient matrix would actually have to be inverted for each region, which can be avoided when interpolating through the individual simplices.

Next: The sequence of triangles Up: Contours for <PLOT> Previous: Three dimensional quadratic approximation