minstesquaresløsning

The term minstesquaresløsning, or least squares solution, refers to a method used in mathematics and statistics to find an approximate solution to an overdetermined system of linear equations. An overdetermined system is one where there are more equations than unknown variables, making it impossible to find a single exact solution that satisfies all equations simultaneously.

The core idea behind the minstesquaresløsning is to find the vector of variables that minimizes the sum of the squares of the differences between the observed values and the values predicted by the system of equations. These differences are often referred to as residuals. By minimizing the sum of these squared residuals, the least squares method provides the "best fit" solution in the sense that it makes the overall error as small as possible.

This technique is widely applied in various fields, including regression analysis, signal processing, and computer vision. For example, in linear regression, the minstesquaresløsning is used to find the coefficients of a linear model that best describes the relationship between a set of independent variables and a dependent variable. The mathematical derivation often involves calculus and linear algebra, leading to a formula that can be used to directly compute the solution.