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Interval Arithmetic (IA), also known as interval analysis, is a technique for numerical computation where each quantity is represented by an interval of floating-pint numbers. Those intervals are added, subtracted, multiplied, etc. in such a way that each computed interval is guaranteed to contain the (unknown) value of the quantity it represents.
The main weakness of IA is that it tends to be too conservative: the intervals it produces are often much wider than the true range of the corresponding quantities, often to the point of uselessness.
To address the problem, a new model for numerical computation, which is called Affine Arithmetic (AA), was proposed in [Andrade et al., 1994]. Like standard IA, AA keeps track of the round-off and truncation errors. In addition, AA keeps track of correlations between those quantities. The extra information enables AA to provide much tighter intervals than standard IA, especially in long computation chains.
This project aims to implement an Affine Arithmetic Library which provides arithmetic operators (e.g addition, subtraction, etc. ) and standard functions (e.g sin, cos, log, etc.). A comparison with IA (that we have implemented) is also to be drawn when applied to various applications.
First year Mathematics courses, C/C++ programming language