Exponential approximation with piecewise linear error criteria

✍ Scribed by J.S. Thorp; R.N. Lewine

• Book ID: 104134220
• Publisher: Elsevier Science
• Year: 1968
• Tongue: English
• Weight: 880 KB
• Volume: 286
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(68)90579-6

✦ Synopsis

The problem of approximating a continuous fun&m on

Ue in&vu1 [O, T] with -~a linear combination of real exponential functti is wnaidered. Rather than restricting the analysis to mathematically well behaved error criteria, such aa lea&-squares, the theory of di&ibutti is used to analyze crikria base& on piecewke linear weigh&ng of the error. For such criteria, it is found that thejirst and second o!erivative.s of the error measure E with respect to the parameters of the approzzinating function can be obtained from exact and easily evaluated formulae. A descent search to find the solution to the approximation problem by minimizing E is thus economically feasible, since rw inaccurate and tim.e-consuming numerical in@dhs are required to produce the needed derivatives. As an example of 8uch a criterion, approximation in the Ll norm is treated.