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Mathematics of Computation

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The calculation of best linear one-sided $L_{p}$ approximations


Author: G. A. Watson
Journal: Math. Comp. 27 (1973), 607-620
MSC: Primary 65D15
DOI: https://doi.org/10.1090/S0025-5718-1973-0343537-8
MathSciNet review: 0343537
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Abstract: The calculation of linear one-sided approximations is considered, using the discrete ${L_p}$ norm. For $p = 1$ and $p = \infty$, this gives rise to a linear programming problem, and for $1 < p < \infty$, to a convex programming problem. Numerical results are presented, including some applications to the approximate numerical solution of ordinary differential equations, with error bounds.


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Keywords: One-sided approximation, <IMG WIDTH="29" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${L_p}$"> approximation, linear programming, convex programming
Article copyright: © Copyright 1973 American Mathematical Society