Numerical Analysis I

Syllabus

• Linear systems: Gaussian elimination and variants; matrix factorizations (LU, LDL*, Cholesky, QR).
• Iterative methods and convergence theorems; Jacobi and Gauss–Seidel iterations; relaxation methods.
• Univariate interpolation: Lagrange and Hermite interpolation; spline interpolation.
• Bernstein polynomials and B-splines (overview and applications).
• Solving nonlinear equations: fixed-point methods (Banach fixed-point framework), Newton method, Broyden method.