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Numerical Methods
Introduction
Numerical computations play an indispensable role in salving real lifemathematical, physical and engineering problems. They have been inuse for centuries even before digital computers appeared on the scene.
Great mathematicians like Gauss, Newton, Lagrange, Fourier and many others in the eighteenth and nineteenth centuries developed numercal techniques which are still widely used. The advent of digital computerhas, however, enhanced the speed and accuracy of numerical computations.
Approximations and Errors In Computing
We cannot use numerical methods and ignore the existence of errors.Errors come in a variety of forms and sizes; some are avoidable, some are not. For example, data conversion and roundoff errors cannot be avoided, but a human error can be eliminated. Although certain errors cannot be eliminated completely, we must at least know the bounds ofthese errors to make use of our final solution. It is therefore essential to know how errors arise, how they grow during the numerical process and how they affect the accuracy of & solution.