Derivative Approximation Task

A Derivative Approximation Task is a differential equation solving task that is a numerical approximation task.

• AKA: Numerical Differentiation, Differential Equation Approximation.
• Context:
  • It can be solved by a Derivative Differentiation System (that implements a derivative differentiation algorithm).
  • …
• Counter-Example(s):
  • Symbolic Differentiation.
  • Exact Derivative Identification.
• See: Differential Equation, Algorithm, Derivative, Automatic Differentiation.

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References

2019

• (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Automatic_differentiation Retrieved:2019-12-16.
  • … Automatic differentiation is distinct from symbolic differentiation and numerical differentiation (the method of finite differences). Symbolic differentiation can lead to inefficient code and faces the difficulty of converting a computer program into a single expression, while numerical differentiation can introduce round-off errors in the discretization process and cancellation. Both classical methods have problems with calculating higher derivatives, where complexity and errors increase. Finally, both classical methods are slow at computing partial derivatives of a function with respect to many inputs, as is needed for gradient-based optimization algorithms. Automatic differentiation solves all of these problems, at the expense of introducing more software dependencies.

2016

• (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/numerical_differentiation Retrieved:2016-9-20.
  • In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.

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