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Fitting Routines
There are four characteristics of the RBF that need to be decided: weights, centers, width, and 
. Each of these can have significant impact on the quality of the resulting fit, and good values for each of them need to be determined. The weights are always determined by specifying the centers, width, and 
, and then solving an appropriate linear system of equations. However, the problem of determining good centers, width, and 
in the first place is far from simple, and is complicated by the strong dependencies among the parameters. For example, the optimal 
varies considerably as the width parameter changes. A global search over all possible center locations, width, and 
is computationally prohibitive in all but the simplest of situations.
To try to combat this problem, the fitting routines come in three different levels.
At the lowest level are the algorithms that choose appropriate centers for given values of width and 
. The centers are chosen one at a time from a candidate set (usually the set of data points or a subset of them). The resulting centers are therefore ranked in a rough order of importance.
At the middle level are the algorithms that choose appropriate values for 
and the centers, given a specified width.
At the top level are the algorithms that aim to find good values for each of the centers, width, and 
. These top-level algorithms test different width values. For each value of width, one of the middle-level algorithms is called that determines good centers and values for 
.
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