Linear Least Squares Analysis

Giriş
Türkçesi sanırım "En Küçük Karaler Yöntemi". Nümerik Analiz dersinde en nefret ettiğim konulardan birisi. Kimin bu yöntemi geliştirdiğine dair bir açıklama şöyle

A fascinating point is that development of least squares came before the discovery of the normal distribution and modern justifications for the use of least squares.

Least squares was developed as a way of combining multiple, imperfect astronomical observations to recover underlying parameters governing the movements of heavenly bodies.

Each astronomical observation defines a linear equation, and with more observations than parameters, the astronomers of the time were faced with an inconsistent system. What to do? Mayer developed a method where observations were separated into kk groups, the equations in each group were averaged together, and then the underlying system could be solved (Stigler 1990). Legendre instead proposed introducing an error term and minimizing the sum of squared error.