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Bibliographic Details
Main Author: Trinity Labo
Format: Recurso digital
Language:
Published: Zenodo 2026
Online Access:https://doi.org/10.5281/zenodo.19019977
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Table of Contents:
  • <div>This work presents a lightweight rational approximation for the inverse square root function together with a Newton-compatible initialization strategy. The method is built around a low-order rational approximation on the normalized interval [1, 2], combined with exact power-of-two scaling to cover the practical range [0.25, 4].</div> <div> </div> <div>The construction is designed for low arithmetic cost, simple implementation, and predictable error behavior. On the normalized interval, the proposed approximation achieves an empirical maximum relative error of about 3.43e-4, while preserving a one-sided error structure that is useful for stable numerical handling. After a single Newton refinement step, the error is reduced to the 1e-7 scale.</div> <div> </div> <div>Rather than targeting formal optimality, this note focuses on practical usefulness: compact evaluation, explicit coefficients, and direct compatibility with fast inverse-square-root workflows. Potential applications include graphics, physics simulation, ray tracing, distance computation, and lightweight numerical kernels.</div>