ABSTRACT
Numerical differentiation is an ill-conditioned problem in the sense that small perturbations in the input can lead to significant differences in the outcome. It is, however important, since many problems require approximations to derivatives. It introduces the concept of discretization error, which is the error occurring when a continuous function is approximated by a set of discrete values. This is also often known as the local truncation error. It is different from the rounding error, which is the error due to the inherent nature of floating point representation. For a given function f(x) : ℝ → ℝ the derivative f′(x) is defined as f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315370217/379fdee0-f6da-47eb-84a6-8ddc64039f18/content/eq1066.tif"/>
