Truncation dimension for linear problems on multivariate function spaces
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The paper considers linear problems on weighted spaces of multivariate functions of many variables. The main questions addressed are the following: when is it possible to approximate the solution for the original function of very many variables by the solution for 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(ε) such that the corresponding error is bounded by a given error demand ε? Surprisingly, k(ε) could be very small even for weights with a modest speed of convergence to zero.
KeywordsMultivariate problems Weighted function spaces Truncation algorithms Truncation dimension
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The authors would like to thank two anonymous referees for their suggestions for improving the paper.
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