numerical-analysis

name	numerical-analysis
description	Numerical approximation methods
license	MIT
compatibility	opencode
metadata	{"audience":"programmers","category":"mathematics"}

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