- Error analysis: Number representation, error types, conditioning and stability
- Interpolation: polynomial and spline interpolation
- Numerical integration and differentiation: order, Newton-Cotes formula, error estimates, Gaussian quadrature, adaptive quadrature, difference formulas
- Linear systems: LU and Cholesky factorization, matrix norms, conditioning
- Linear least squares problems: normal equations, Gram.Schmidt and Householder orthogonalization, singular value decomposition, regularization
- Eigenvalue problems: power iteration, inverse iteration, QR algorithm
- Nonlinear systems of equations: Fixed point iteration, root-finding algorithms for real-valued functions, Newton and Quasi-Newton methods for systems
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