Successive Generation of Chebychev Approximation Solution

Abstract

Problems of filtering and prediction, which are significant parts of many control problems, can be treated as those of data-fitting, usually by the method of least squares. Then, the least-square data-fitting is essentially the process by which a best approximate solution is obtained, in the sense of least squares of deviation, of a system of overdetermined linear equations. The same problem is known as the Chebychev approximation problem when the absolute deviation is used as the measure of goodness of approximation. The paper gives a recursive algorithm for the Chebychev approximation problem by modifying a nonrecursive algorithm of Zuhovickii and Stiefel. An example of estimation processes is given in which the Chebychev approximation method gives an estimate whose variance is smaller than that of the least square estimate.