# Numerical Analysis Foundations

> Floating point, conditioning, stability, convergence, error budgets, choosing a scheme.

- Skill: `poly-gents/numerical-analysis-foundations` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add poly-gents/numerical-analysis-foundations`
- Raw SKILL.md: https://api.skillmd.com/api/skills/poly-gents/numerical-analysis-foundations/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: poly-gents (https://skillmd.com/u/poly-gents)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/poly-gents/numerical-analysis-foundations

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# Numerical analysis foundations

- State the **problem class** (root-finding, IVP, BVP, eigenvalue, optimization, quadrature) before picking a method.
- Discuss **conditioning vs stability** explicitly: a stable algorithm on an ill-conditioned problem still loses digits.
- Pick the order of convergence you actually need; quote the cost.
- For floating-point work, watch catastrophic cancellation, subtraction near equal values, and accumulated round-off.
- Always include a **convergence check** (refine the grid / shrink the step) and an **error estimate** before quoting a number.