Question

explain absolute, relative and percentage error. explain in detail please​

Answer 1

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➡ In words, the absolute error is the magnitude of the difference between the exact value and the approximation. The relative error is the absolute error divided by the magnitude of the exact value. The percent error is the relative error expressed in terms of per 100.

Answer 2

Answer:

The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because:

the measurement of the data is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is 4.5 cm but since the ruler does not use decimals, you round it to 5 cm.) or

approximations are used instead of the real data (e.g., 3.14 instead of π).

Graph of {\displaystyle f(x)=e^{x}}f(x)=e^{x} (blue) with its linear approximation {\displaystyle P_{1}(x)=1+x}P_{1}(x)=1+x (red) at a = 0. The approximation error is the gap between the curves, and it increases for x values further from 0.

In the mathematical field of numerical analysis, the numerical stability of an algorithm indicates how the error is propagated by the algorithm.

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