Syllabus
Solving liner systems, direct methods: Gauss elimination, LU-decomposition, pivoting, Cholesky decompositon.
Least Squares: data fitting, linear least squares, normal equation, pseudoinverse, QR-decomposition.
Nonlinear systems: Fixed Point Theorem (contraction mapping), Newton's Method, Newton-like methods.
Function minimization: Nelder-Mead Method, Method of Steepest Descent, Conjugate Gradient Method.
Interpolation: Lagrange Interpolating Polynomial, Chebyshev Polynomial, splines.
Ordinary Differential Equations: initial value problem, Euler Method, implicit Euler Method, Runge-Kutta Method.
Eigenvalue problems: a primer (eigenvalue, eigenvector, Characteristic Polynomial, multiplicity, Similar Matrices, Jordan canonical form), Power Method, Inverse iteration, QR algoritmus.
Iterative Methods (linear systems): large sparse matrices, Gauss-Seidel Method, Successive Overrelaxation Method, Conjugate Gradient Method, preconditioning.
Annotation
The first course of numerical analysis for students of Financial Mathematics.