intervallaritmetikk

Interval arithmetic is a mathematical technique for numerical computation that represents numbers as intervals rather than exact values. This approach provides a way to handle uncertainty and rounding errors in calculations. In interval arithmetic, each number is represented as a range [a, b] where a is the lower bound and b is the upper bound.

The fundamental operations of addition, subtraction, multiplication, and division are extended to intervals. For example, the sum of two intervals [a, b] and [c, d] is [a+c, b+d]. Multiplication is more complex, as the result depends on the signs of the endpoints.

Interval arithmetic has applications in various fields including numerical analysis, computer graphics, control systems, and scientific computing. It is particularly valuable for verifying the correctness of numerical algorithms and for solving problems with uncertain or incomplete data.

One of the main advantages of interval arithmetic is its ability to provide guaranteed bounds on the result of computations. However, it can sometimes produce overly conservative bounds, especially in complex calculations with multiple operations. This mathematical approach was formally developed in the 1950s and has since become an important tool in reliable scientific computing.