plural of Lagrange

A surname from French.

A surname from French, variant of Lagrange / A town in Lee County, Arkansas, United States. / A city, the county seat of Troup County, Georgia, United States.

(mathematics) a set of equations of motion of a mechanical system which relate the kinetic energy of the system to its generalized coordinates

(astrophysics, orbital mechanics) A point in an orbital configuration of a two-body system where a small object affected only by gravity can theoretically be stationary relative to the two larger objects.

plural of Lagrange point

A county of Indiana, United States. County seat: LaGrange. Named after Château de la Grange-Bléneau, the home of Gilbert du Motier, Marquis de Lafayette.

(mathematics) For a given set of points (x_j,y_j) with no two x_j values equal, the polynomial of lowest degree that assumes at each value x_j the corresponding value y_j, so that the functions coincide at each point.

plural of Lagrange polynomial

(mathematics) A formula which when given a set of n points (x_i,y_i), gives back the unique polynomial of degree (at most) n − 1 in one variable which describes a function passing through those points. The formula is a sum of products, like so: ∑ᵢⁿy_i∏_(j ne i)x-x_j/x_i-x_j. When x=x_i then all terms in the sum other than the iᵗʰ contain a factor x-x_i in the numerator, which becomes equal to zero, thus all terms in the sum other than the iᵗʰ vanish, and the iᵗʰ term has factors x_i-x_j both in the numerator and denominator, which simplify to yield 1, thus the polynomial should return y_i as the function of x_i for any i in the set 1,...,n.