Basic Information
Introduction. Numerical Instability, Numerical Errors, Loss Of Significant Digits (cancellation). Iterative Solution of Scalar Nonlinear Equations# Bisection Method, Newton-raphson Method, Secant Method, Convergence Analysis. Approximation of Functions# Norms and Seminorms, Inner Product, Orthogonal Systems, Least Squares, Polynomial Interpolation, Chebyshev Polynomials And Their Use in Interpolation. Discrete Approximation Of Derivatives, Richardson Extrapolation, Numerical Integration. Linear Systems# Gaussian Elimination and Lu-decomposition, Positive Definite Matrices, Generalized Inverse, Matrix Norms, Elementry Iterative Methodes For Linear Systems, Newton's Method For Nonlinear Systems. Orthogonality, Qr-decomposition, Svd - Decomposition, Gershgorin's Theorem, Power Method. Fourier Transform And The Fft Algorithm.