A computational study of a class of recursive inequalities

IF 0.3 Q4 LOGIC
Morenikeji Neri, Thomas Powell
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引用次数: 0

Abstract

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results concerning rates of convergence, setting out conditions under which computable rates are possible, and when not, providing corresponding rates of metastability. We then demonstrate how the aforementioned quantitative results can be applied to extract computational information from a range of proofs in nonlinear analysis. Here we provide both a new case study on subgradient algorithms, and give overviews of a selection of recent results which each involve an instance of our main recursive inequality. This paper contains the definitions of all relevant concepts from both proof theory and mathematical analysis, and as such, we hope that it is accessible to a general audience.
一类递归不等式的计算研究
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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
2
审稿时长
35 weeks
期刊介绍: "Journal of Logic and Analysis" publishes papers of high quality involving interaction between ideas or techniques from mathematical logic and other areas of mathematics (especially - but not limited to - pure and applied analysis). The journal welcomes papers in nonstandard analysis and related areas of applied model theory; papers involving interplay between mathematics and logic (including foundational aspects of such interplay); mathematical papers using or developing analytical methods having connections to any area of mathematical logic. "Journal of Logic and Analysis" is intended to be a natural home for papers with an essential interaction between mathematical logic and other areas of mathematics, rather than for papers purely in logic or analysis.
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