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Show CHAPTER 3 COMBINED METHODS Now that all of the basic tools are in place, some interesting interactions can be investigated. Some simple combinations will be examined first, which are either methods in their own right, or are subparts of a larger method. Combining methods is not straightforward; if the interaction of two methods is not well understood, it is impossible to predict the results when more are combined. It is unlikely that any one combined method will be superior for all uses. The methods discussed vary from O(n) to 0(n3), and the nonlinear methods range from quadratic convergence to much slower convergence, so the speed of a combined method will be as important as the compactness or shape of the approximation produced. In selecting which parts of each of the methods to use, one must balance the need for speed, guaranteed convergence and predictable computation time with the need for results that are optimal in some sense, i.e., compactness of representation, smoothness, closeness to data, et cetera. The final methods combine most or all of the features discussed in Table 1, on page 14. It is difficult to make a fair comparison of some of the author's combined methods with other approaches, since many authors address only one part of the problem [4, 22, 21, 14, 6] and assume that the rest* is given, but an effort will be made to do this. The comparison in section 3.7 of a range of combined methods of varying power provides some interesting insight. * A "good" parametrization, for instance. |
