numerical-analysis

## 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