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BRICS Report Series
In this survey paper we start with a discussion how functionals of finite type can be used for the proof-theoretic extraction of numerical data (e.g. effective<br />uniform bounds and rates of convergence) from non-constructive proofs in numerical analysis. We focus on the case where the extractability of polynomial bounds is guaranteed.<br />This leads to the concept of hereditarily polynomial bounded analysis (PBA). We indicate the mathematical range of PBA which turns out to be surprisinglydoi:10.7146/brics.v4i30.18956 fatcat:q2kvu7ah6fhoxky2o6uykd6mvq