Numerical Analysis - General Introduction

General Introduction

The overall goal of the field of numerical analysis is the design and analysis of techniques to give approximate but accurate solutions to hard problems, the variety of which is suggested by the following.

• 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 equations numerically.
• Hedge funds (private investment funds) use tools from all fields of numerical analysis to attempt to calculate the value of stocks and derivatives more precisely than other market participants.
• 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 actuarial analysis.

The rest of this section outlines several important themes of numerical analysis.