Broadening classic methods of approximation by implicit functions enables approximation of a set by disconnected figures, e.g. approximation of two or more points simultaneously. As a result it's possible to determine in exact way the 'centers of mass concentration' of an analyzed set - that is to indicate the areas of the set of big congestion of elements. What might be problematic is to determine the proper amount of points to approximate a certain set. How to verify the thesis that two point approximation is more 'proper' than one point approximation? Or to put it in a more general way: how to verify the thesis that it's better to approximate a set by the k-points? In the article the concept of a partial variance is introduced, as a kind of generalization of set variance. The partial variance proves to be a useful tool which enables among others, answering the above questions. It's bound...

more

Broadening classic methods of approximation by implicit functions enables approximation of a set by disconnected figures, e.g. approximation of two or more points simultaneously. As a result it's possible to determine in exact way the 'centers of mass concentration' of an analyzed set - that is to indicate the areas of the set of big congestion of elements. What might be problematic is to determine the proper amount of points to approximate a certain set. How to verify the thesis that two point approximation is more 'proper' than one point approximation? Or to put it in a more general way: how to verify the thesis that it's better to approximate a set by the k-points? In the article the concept of a partial variance is introduced, as a kind of generalization of set variance. The partial variance proves to be a useful tool which enables among others, answering the above questions. It's bound to the method of approximation by disconnected figures, being its valuable completion.

COLLAPSE