A note on the semi-infinite programming approach to complex approximation

Authors:
Roy L. Streit and Albert H. Nuttall

Journal:
Math. Comp. **40** (1983), 599-605

MSC:
Primary 49D39; Secondary 30E10, 90C05

MathSciNet review:
689476

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Abstract: Several observations are made about a recently proposed semi-infinite programming (SIP) method for computation of linear Chebyshev approximations to complex-valued functions. A particular discretization of the SIP problem is shown to be equivalent to replacing the usual absolute value of a complex number with related estimates, resulting in a class of quasi-norms on the complex number field , and consequently a class of quasi-norms on the space consisting of all continuous functions defined on , *Q* compact. These quasi-norms on are estimates of the norm on and are useful because the best approximation problem in each quasi-norm can be solved by solving (i) an ordinary linear program if *Q* is finite or (ii) a simplified SIP if *Q* is not finite.

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0689476-0

Article copyright:
© Copyright 1983
American Mathematical Society