axiolid-numeric

General numeric routines that geometry algorithms build on: bracketed root finding (Brent) and every real root of a polynomial in an interval, adaptive Gauss-Kronrod quadrature and fixed Gauss-Legendre rules, LU, Cholesky and column-pivoted QR solves, linear least squares with and without equality constraints, Levenberg-Marquardt for nonlinear least squares, and Brent's bounded scalar minimiser. Each result carries a bracket, an error estimate or a condition estimate, and each iterative routine says whether it met its tolerance. Non-finite input, singular or rank-deficient matrices and unbracketed roots are refused by name. Values are plain f64; there are no geometry types and no dependencies.

cargo add axiolid-numeric

• API documentation: docs.rs/axiolid-numeric
• Reference page: axiolid.github.io/kernel
• Source and issues: github.com/axiolid/kernel

Design notes

Polynomial roots are isolated through the roots of the derivative, and a sign is trusted only where the value exceeds a rigorous bound on its own rounding error. Where it does not (a multiple root, a cluster closer than f64 separates) the answer is an unresolved region with the most roots it can hold, not a guessed count. For exact decisions on integer polynomials use axiolid-exact.

Older inline routines elsewhere in the workspace (bisection and an 8-point Gauss-Legendre rule in axiolid-evaluate, the interpolation solve in axiolid-nurbs) are unchanged; new code should use this crate.