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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A note on the semi-infinite programming approach to complex approximation
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by Roy L. Streit and Albert H. Nuttall PDF
Math. Comp. 40 (1983), 599-605 Request permission

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 $\mathbf {C}$, and consequently a class of quasi-norms on the space $C(Q)$ consisting of all continuous functions defined on $Q \subset {\mathbf {C}}$, Q compact. These quasi-norms on $C(Q)$ are estimates of the ${L_\infty }$ norm on $C(Q)$ 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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 599-605
  • MSC: Primary 49D39; Secondary 30E10, 90C05
  • DOI: https://doi.org/10.1090/S0025-5718-1983-0689476-0
  • MathSciNet review: 689476