Course Contents

Solution of System of Linear Equations; Gaussian elimination method, Triangular decomposition method and its various forms, Iterative methods for solving diagonally dominant system of linear equations, Jacobi method, Gauss-Seidel method, Comparison with Jacobi method, SOR method using different values of parameter, Ill-condition systems and condition number. Eigenvalues and Eigenvectors of a Matrix; Definitions and examples, Geometric interpretation of eigenvalues and eigenvectors, Gerschgorin Circle Theorem and its application to different matrices, Power method and its application, Inverse power method. Interpolation; Lagrange interpolation, Newton’s divided difference formula, Finite difference operators and their relationship, Newton’s forward difference interpolation formulas, Newton’s backward difference interpolation formulas, Hermite Interpolation, Cubic Splines; Definition and examples, Construction of natural and clamped cubic splines

Course Learning Outcomes

Given a reasonable mathematical problem, graduates from this course will be able to: 1. devise an algorithm to solve it numerically; 2. implement this algorithm; 3. describe classic techniques and recognize common pitfalls in numerical analysis; 4. analyze an algorithm’s accuracy, efficiency and convergence properties.