Introduction to Numerical Analysis/Computations

 


COMSATS University Islamabad, Pakistan


 

NUMERICAL COMPUTATIONS

What is numerical Computation?

Numerical Computation is concerned with the derivation, analysis, and implementation of methods for obtaining reliable numerical answers to complex mathematical problems. In other words, NC is the subject concerned with the construction, analysis, and use of algorithms for the numerical solutions of mathematical problems to the given degree of numerical accuracy.

When mathematical problems can be solved analytically, their solution may be exact, but more frequently, there may not be a known method of obtaining its solution. e.g.

Many more such examples can be cited for which solutions by analytical means are either impossible or may be so complex that they are quite unsuitable for practical purposes.

    During the last century, numerical techniques have witnessed a veritable explosion in research, both in their application to complex mathematical systems and in the very development of these techniques. At many places in this course, we will compare numerical techniques with analytical techniques, and point out various problems which cannot be solved through analytical techniques, and to which numerical techniques provide quite good approximate solutions. Many researchers are using numerical techniques to investigate research problems.



 

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