Class: 3rd Numerical Methods


Errors in numerical calculations


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Numerical Methods new 1

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Errors in numerical calculations, Sources of errors, significant digits and numerical instability

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Numerical solution of polynomial and transcendental equations - bisection method - method of false position

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Newton-Raphson method - fixed-point iteration - rate of convergence of these methods - iteration based on second degree equation - the Muller’s method - Chebyshev method

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Graeffe’s root squaring method for polynomial equations - Bairstow’s method for quadratic factors in the case of polynomial equations

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Solutions of system of linear algebraic equations, Direct methods - gauss and gauss - Jordan methods - Crout’s reduction method – error analysis

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Iterative methods - Jacobi’s iteration - Gauss-seidel iteration - the relaxation method - convergence analysis

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Solution of system of nonlinear equations by Newton- Raphson method

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power method for the determination of Eigen values - convergence of power method

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