ffsshhttiikk 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