High-Precision Companion Matrix Root Finder
High-Precision Companion Matrix Root Finder
A robust polynomial solver leveraging arbitrary-precision floating-point arithmetic to compute roots of ill-conditioned polynomials. This tool primarily addresses rounding and finite-precision issues present in standard 64-bit floating-point implementations by constructing and solving a companion matrix within the mpmath environment.
The solver cannot eliminate the intrinsic mathematical ill-conditioning of certain polynomials, but it can significantly reduce the numerical errors caused by rounding, making the computed roots far more reliable.
It features modular code structure, residual checks, and robust input validation to improve usability and reliability.
Key Idea
The solver does not attempt to solve the fundamental conditioning problem of polynomial root finding.
Instead, it focuses on reducing numerical rounding errors using high‑precision arithmetic, which in practice leads to far more reliable root approximations for difficult polynomials.
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