MTL509: Numerical Analysis

4 Credits (3-1-0)

Numerical Algorithms and errors, Floating point systems, Roundoff error accumulations. Interpolation: Lagrange Interpolation Newton’s divided difference interpolation. Finite differences. Hermite Interpolation. Cubic splines. Numerical differentiation. Numerical Integration: Newton cotes formulas, Gaussian Quadrature composite quadrature formulas

Approximation: Least squares approximation, minimum maximum error techniques. Legendre and Chebyshev polynomials. Solution of Nonlinear equations: Fixed point iteration,bisection, Secant,Regula-Falsi, Newton-Raphson methods. Solution of linear systems: Direct methods, Gauss elimination, LU and Cholesky factorizations. Iterative methods – Jacobi, Gauss- Seidel and SOR methods. System of nonlinear equation, Eigen-Value problems: Power and Inverse power method. Numerical Solution of ODE. Taylor series, Euler and Runge-Kutta methods.