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The Lagrange multiplier theorem states that at any local maximum (or minimum) of the function evaluated under the equality constraints, if constraint qualification applies (explained below), then the gradient of the function (at that point) can be expressed as a linear combination of the gradients of the constraints (at that point), with the ...
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Joseph-Louis Lagrange (1736–1813). In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action).
Joseph-Louis Lagrange [a] (born Giuseppe Luigi Lagrangia [5] [b] or Giuseppe Ludovico De la Grange Tournier; [6] [c] 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange [7] or Lagrangia, [8] was an Italian mathematician, physicist and astronomer, later naturalized French.
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Lagrange's theorem raises the converse question as to whether every divisor of the order of a group is the order of some subgroup. This does not hold in general: given a finite group G and a divisor d of | G |, there does not necessarily exist a subgroup of G with order d .
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Lagrange and other interpolation at equally spaced points, as in the example above, yield a polynomial oscillating above and below the true function. This behaviour tends to grow with the number of points, leading to a divergence known as Runge's phenomenon ; the problem may be eliminated by choosing interpolation points at Chebyshev nodes .