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Indian Institute of Science Education and Research Bhopal

MTH 408: Numerical Analysis (4)

Pre-requisites: MTH 303 Real Analysis I

Round off errors and computer arithmetic

Interpolation: Lagrange interpolation, divided differences, Hermite interpolation, splines, numerical differentiation, Richardson extrapolation

Numerical Integration: trapezoidal, Simpsons, Newton-Cotes, Gauss quadrature, Romberg integration, multiple integrals

Solution of linear algebraic equations: direct methods, Gauss elimination, pivoting, matrix factorizations

Iterative methods: matrix norms, Jacobi and Gauss-Siedel methods, relaxation methods

Computation of eigenvalues and eigenvectors: power method, householders method, QR algorithm

Numerical solutions of non-linear algebraic equations: bisection, secan and Newton's, zeroes of polynomials

Suggested Books:

• R. L. Burden, D. J. Faires, Numerical Analysis
• E. K. Blum, Numerical Analysis and Computation, Theory and Practice, Dover, 2010
• S. D. Conte, C. De Boor, Elementary Numerical Analysis,third edition, McGraw-Hill, 1980
• D. M. Young, R. T. Gregory, A Survey of Numerical Mathematics, volumes 1 and 2, Dover, 1988

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