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(this article needs work, more content, explanation of the Gauss method)
Least squares is a mathematical optimization technique that attempts to find a
"best fit" to a set of data by attempting to minimize the sum of the squares of the differences (called residuals) between the fitted
function and the data.
It is commonly used in curve fitting. Many other optimization problems
can also be expressed in a least squares form, either minimizing energy or maximizing
entropy.
See linear regression and Gauss-Markov theorem. The Gauss-Markov theorem says that least-squares estimators are in a
certain sense optimal.
To use the method of least squares we use a function f(x), containing some number of unknown constants (for
instance f(x) = mx + b, where m and b are not yet known), and find the
values of m and b that minimize the sum of the squares of the residuals (that is, the sum of terms of the form
(yi − f(xi))2). We then have the equation for
the curve, y = f(x), of the required form, that best fits the data points
(xi, yi).
For linear functions f see linear least squares.
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