Numerical Analysis

Numerical approximation methods

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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

NeuralBlitz/Agent-Gateway/tree/main/agent-gateway/skills/user/numerical-analysis commit 9b7f5decec

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