NUMERICAL ANALYSIS II

 
Approximation of Functions and Modelling of Data: Interpolation by linear and cubic splines. Trigonometric polynomials. Orthogonal polynomials and least-squares approximations. Least-squares fits.
Numerical Integration: Gaussian quadrature. Adaptive quadrature. Multiple integrals.
Solution of Linear Systems of Equations:QR-decomposition. Least-squares solution of overdetermined linear systems. Basic iterative methods. Jacobi method and Gauss-Seidel method. Implementation of iterative methods. Conjugate gradient Algorithm
Eigenvalue problem. Localization of eigenvalues. The power method. The inverse power method. Eigenvalues and eigenvectors of a Tridiagonal matrix. Reduction of a general matrix to Hessemberg form. Householder transformations. The QR Algorithm for real Hessemberg matrices.
Solution of Nonlinear Equations: Secant method, False Position method. Newton’s method in two variables. Zeros of polynomials. Fixed-point methods. Rate of convergence.
Numerical Solution of Ordinary Differential Equations: Linear multistep methods. Adams methods. Predictor-corrector methods. Order and convergence for multistep methods. Finite-difference methods. Collocation methods.