Editing Numerical analysis (section)

==Applications==
The overall goal of the field of numerical analysis is the design and analysis of techniques to give approximate but accurate solutions to a wide variety of hard problems, many of which are infeasible to solve symbolically:

* Advanced numerical methods are essential in making [[numerical weather prediction]] feasible.
* Computing the trajectory of a spacecraft requires the accurate numerical solution of a system of ordinary differential equations.
* Car companies can improve the crash safety of their vehicles by using computer simulations of car crashes. Such simulations essentially consist of solving [[partial differential equation]]s numerically.
* In the financial field, (private investment funds) and other financial institutions use [[quantitative finance]] tools from numerical analysis to attempt to calculate the value of [[share capital|stock]]s and [[Derivative (finance)|derivatives]] more precisely than other market participants.<ref>
Stephen Blyth.
[https://books.google.com/books?id=SXbcAAAAQBAJ "An Introduction to Quantitative Finance"].
2013.
page VII.
</ref>
* Airlines use sophisticated optimization algorithms to decide ticket prices, airplane and crew assignments and fuel needs. Historically, such algorithms were developed within the overlapping field of [[operations research]].
* Insurance companies use numerical programs for [[Actuary|actuarial]] analysis.