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Applied Mathematical Methods by Bhaskar Dasgupta

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7

Numerical Aspects in Linear Systems

In this chapter, we concentrate on numerical aspects in the solution of linear systems. With a brief introduction to norms and condition number, we examine the connection between ill-conditioning of the coefficient matrix and the sensitivity of the corresponding solution to the given data. We also have an introductory look at rectangular systems of equations and develop their working solutions. Finally, for the sake of completeness, we close with a brief discussion on numerical iterative techniques for solving linear systems.

Norms and Condition Numbers

The norm of a vector is a measure of its size or magnitude. The usual magnitude or standard norm

is often referred to as the Euclidean norm, in connection ...

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