# Numerical Analysis

> Numerical approximation methods

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

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## What I do
- Implement numerical integration (quadrature)
- Solve nonlinear equations numerically
- Approximate derivatives and integrals
- Interpolate data points
- Solve linear systems iteratively
- Analyze numerical stability and error

## When to use me
When analytical solutions are unavailable and numerical approximation is needed.

## Key Concepts
- **Numerical Error**: Truncation (method) + rounding (floating point) errors
- **Newton-Raphson**: x_{n+1} = x_n - f(x_n)/f'(x_n) for root finding
- **Gaussian Quadrature**: Optimal nodes/weights for exact polynomial integration
- **Lagrange Interpolation**: Polynomial through given points
- **Condition Number**: κ = ||A||·||A^{-1}|| measures problem sensitivity
- **Iterative Solvers**: Jacobi, Gauss-Seidel, Conjugate Gradient methods