August 26, 2025

The Best Two-Term Underapproximation Using Numbers From Fibonacci-Type Sequences

Key Points

The best two-term underapproximation is identified for specific θ values within (0,1].
Optimal sets of θ were determined, enhancing the understanding of two-term underapproximations.
This research employs Fibonacci and Lucas sequences, applying greedy algorithms to analyze numerical outcomes.
Implications suggest that these findings may improve calculations related to underapproximations in various mathematical contexts.

Abstract

This paper studies the greedy two-term underapproximation of θ∈(0,1] using reciprocals of numbers from a Fibonacci-type sequence (cn)n=1∞. We find the set of θ whose greedy two-term underapproximation is the best among all two-term underapproximations using 1/cn's. We then derive a neat description of the set when (cn)n=1∞ is the Fibonacci sequence or the Lucas sequence.

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Cite This Study

Mark Shiliaev (Tue,) studied this question.

synapsesocial.com/papers/68af620aad7bf08b1eae3101 https://doi.org/https://doi.org/10.1080/00150517.2025.2490766

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