Adrien-marie legendre pronunciation

In , Legendre published the first description of the method of least squares as an algebraic fitting procedure.

Legendre equation

It was subsequently justified on statistical grounds by Gauss and Laplace. Adrien-Marie Legendre was born in Paris France. He was the son of well-to-do parents and could afford to devote himself full-time to scientific research until the rigours of the French Revolution dissipated the family fortunes and made it necessary for him to work for a living as a minor official in a variety of administrative posts.

It is fortunate for the development of science in France that Fourier, Laplace , and Legendre amongst others were able to escape with their lives.

Legendre transform

Thus it was in the year of the battles of Austerlitz and Jena, that Legendre, then 52 years old, published his monograph outlining the fundamental results on the method of least squares. The geodetic work published by Legendre during this period was so important that it merited four chapters in Todhunter's History of Mathematical Theories of Attraction and the Figure of the Earth However, Legendre resigned from the second commission in March In Laplace became Minister of the Interior and Legendre succeeded him as the examiner in mathematics of students assigned to the artillery corps.

In Legendre voluntarily resigned this position on half pay but was subsequently stripped of his pension when he refused to vote for the official candidate in an election to a seat in the Institut de France. In the second half of the eighteenth century astronomers, geodesists, and other practical scientists were obliged to perfect their own methods for solving systems of equations in which there were more observations than unknowns.

From antiquity until the only possible solution to this problem was to arrange that there should be as many equations as there were unknowns. In Tobias Mayer suggested that the unknowns should be determined by setting certain sums of equations equal to zero; in Boscovich proposed that the unknowns should be determined by minimising the sum of the absolute errors subject to an adding-up constraint; and in Laplace suggested that the unknowns should be determined by minimising the largest absolute error.

Legendre's method of least squares clearly represents a further contribution in this practical tradition as his argument is entirely algebraic and has no statistical content. Legendre's discussion of the method of least squares is to be found in the first four pages pp. By contrast with the Boscovich and minimax procedures which, in practice, seem to have been restricted to the case of two unknowns, the method proposed by Legendre could be applied to any number of linear equations in any lesser number of unknowns.

Instead of choosing values for the unknowns to minimise the largest absolute error or to minimise the sum of the absolute errors, he chose these values to minimise the sum of the squared errors.