A note on the semiinfinite programming approach to complex approximation
Authors:
Roy L. Streit and Albert H. Nuttall
Journal:
Math. Comp. 40 (1983), 599605
MSC:
Primary 49D39; Secondary 30E10, 90C05
MathSciNet review:
689476
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Abstract: Several observations are made about a recently proposed semiinfinite programming (SIP) method for computation of linear Chebyshev approximations to complexvalued 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 quasinorms on the complex number field , and consequently a class of quasinorms on the space consisting of all continuous functions defined on , Q compact. These quasinorms on are estimates of the norm on and are useful because the best approximation problem in each quasinorm 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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 G. A. Watson, Approximation Theory and Numerical Methods, Wiley, New York, 1980. MR 574120 (82e:41001)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198306894760
PII:
S 00255718(1983)06894760
Article copyright:
© Copyright 1983
American Mathematical Society
