2024/12/16 by Vijay Prakash S, S, Vijay Prakash · 2 citations
Mathematics · #FOS: Computer and information sciences #Functional Equations Stability Results #Machine Learning (cs.LG) #Mathematics and Applications #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2412.16191
openalex publication_date 2024/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines, in this work, are made to be bounded by introducing a parametric nonlinear term that is positive. The straight lines are transformed into bounded nonlinear curves that become unbounded at a much slower rate than the independent variable. This transforming equation can be expressed as a continued fraction of straight lines. The continued fraction is real-valued and converges to the solutions of the transforming equation. Following Euler's method, the continued fraction has been reduced into an infinite series. The usefulness of the bounding nature of continued fraction is demonstrated by solving the problem of image classification. Parameters estimated on the Fashion-MNIST dataset of greyscale images using continued fraction of regression lines have less variance, converge quickly and are more accurate than the linear counterpart. Moreover, this multi-dimensional parametric estimation problem can be expressed on xy- plane using the parameters of the continued fraction and patterns emerge on planar plots.