Abstract
Continuous functions of two real variables are approximated on compact domains in the uniform norm by the classes NOM of nomographic functions which appear as approximation subspaces in bivariate approximation theory, in the theory of integral equations., functional equations, scalings of matrices, Goursat-type problems for the wave equation. The approximation problem is converted into the negative cycle problem in a properly chosen family of weighted directed graphs, and a version of the Ford-Bellman algorithm for finding the shortest paths leads to constructive proofs of new characterization and existence theorems.
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Golitschek, M.v. (1984). Shortest Path Algorithms for the Approximation by Nomographic Functions. In: Butzer, P.L., Stens, R.L., Sz.-Nagy, B. (eds) Anniversary Volume on Approximation Theory and Functional Analysis. ISNM 65: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 65. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5432-0_27
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