2019/07/31 by Daniel E. Martin, Martin, Daniel E.
Computer Science · Mathematics · #11A05 #11A55 #11H31 #11J17 #11J70 #11R11 #11Y16 #11Y40 #11Y65 #40A15 #52C05 #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Number Theory (math.NT) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.1908.00121
openalex publication_date 2019/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose and study a generalized continued fraction algorithm that can be executed in an arbitrary imaginary quadratic field, the novelty being a non-restriction to the five Euclidean cases. Many hallmark properties of classical continued fractions are shown to be retained, including exponential convergence, best-of-the-second-kind approximation quality (up to a constant), periodicity of quadratic irrational expansions, and polynomial time complexity.