Truncation Dimension for Linear Problems on Multivariate Function Spaces

Aicke Hinrichs, Peter Kritzer, Friedrich Pillichshammer, G. W. Wasilkowski

Published 2017-01-24Version 1

The paper considers linear problems on weighted spaces of high-dimensional functions. The main questions addressed are: When is it possible to approximate the original function of very many variables by the same function; however with all but the first $k$ variables set to zero, so that the corresponding error is small? What is the truncation dimension, i.e., the smallest number $k=k(\varepsilon)$ such that the corresponding error is bounded by a given error demand $\varepsilon$? Surprisingly, $k(\varepsilon)$ could be very small.