Approximation

Approximations might also be used if incomplete information prevents use of exact representations.

The type of approximation used depends on the available information, the degree of accuracy required, the sensitivity of the problem to this data, and the savings (usually in time and effort) that can be achieved by approximation.

Approximation theory is a branch of mathematics, and a quantitative part of functional analysis.

Numerical approximations sometimes result from using a small number of significant digits.

The approximately equals sign, ≈, was introduced by British mathematician Alfred Greenhill in 1892, in his book Applications of Elliptic Functions.

Some problems in physics are too complex to solve by direct analysis, or progress could be limited by available analytical tools.

Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly.

This is extremely difficult due to the complex interactions of the planets' gravitational effects on each other.

In the first iteration, the planets' gravitational interactions are ignored, and the star is assumed to be fixed.

If a more precise solution is desired, another iteration is then performed, using the positions and motions of the planets as identified in the first iteration, but adding a first-order gravity interaction from each planet on the others.

Simulations of the motions of the planets and the star also yields more accurate solutions.

Within the European Union (EU), "approximation" refers to a process through which EU legislation is implemented and incorporated within Member States' national laws, despite variations in the existing legal framework in each country.

Approximation is a key word generally employed within the title of a directive, for example the Trade Marks Directive of 16 December 2015 serves "to approximate the laws of the Member States relating to trade marks".