Abstract
There are different possibilities to approximate a continuous function of n independent real variables by functions of fewer veriables and their combinations. Here we consider several special types which occur in the applications: The sum-type, product-sum-type, parametric type and combined type. For these types applications, especially to partial differential equations are given. For the product-sum-type approximation an inclusion theorem for the minimal distance is given which in special cases allows us to prove the optimality of a given approximation.
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Collatz, L. (1972). Approximation by functions of fewer variables. In: Everitt, W.N., Sleeman, B.D. (eds) Conference on the Theory of Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066916
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DOI: https://doi.org/10.1007/BFb0066916
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