A survey of published programs for best approximation

✍ Scribed by Charles B. Dunham

• Publisher: Elsevier Science
• Year: 1979
• Tongue: English
• Weight: 288 KB
• Volume: 5
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/0771-050x(79)90010-x

✦ Synopsis

We list and discuss published programs for best approximation of functions by linear and nonlinear families in all standard norms. In this note we list and discuss the published programs for obtaining best approximations. Let X be a set on which we wish to approximate. Most sets will be finite (an equivalent term is discrete). Let II II be a norm on the continuous functions on X. Let G be a familiy of continuous functions on X. For a given basis ~¢1, "", en ), the linear family G is the set of all functions of the form n r/A,x) 1 akekCX)"

The problem of best approximation is given a continuous function f, to find g* to minimize e(g) = IIf-gll over g~G. Such g* is called a best approximation to f. Discrete linear approximation problems are sometimes formulated as solution of an overdetermined system of linear equations Ax= b with respect to a norm where aij = ~j(xi) and b i = f(xi).