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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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:
  • MathSciNet review: 689476