Inverse Distance Weighting - Definition of The Problem

Definition of The Problem

The expected result is a discrete assignment of the unknown function in a study region:

where is the study region.

The set of known data points can be described as a list of tuples:

The function is to be "smooth" (continuous and once differentiable), to be exact and to meet the user's intuitive expectations about the phenomenon under investigation. Furthermore, the function should be suitable for a computer application at a reasonable cost (nowadays, a basic implementation will probably make use of parallel resources).

Read more about this topic:  Inverse Distance Weighting

Famous quotes containing the words definition of the, definition of, definition and/or problem:

    The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.
    Jean Baudrillard (b. 1929)

    The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.
    Ralph Waldo Emerson (1803–1882)

    Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.
    Nadine Gordimer (b. 1923)

    The great problem of American life [is] the riddle of authority: the difficulty of finding a way, within a liberal and individualistic social order, of living in harmonious and consecrated submission to something larger than oneself.... A yearning for self-transcendence and submission to authority [is] as deeply rooted as the lure of individual liberation.
    Wilfred M. McClay, educator, author. The Masterless: Self and Society in Modern America, p. 4, University of North Carolina Press (1994)