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Some problems in optimally stable Lagrangian differentiation

1974
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Mathematics of Computation
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In many practical problems in numerical differentiation of a function f(x) that is known, observed, measured, or found experimentally to limited accuracy, the computing error is often much more significant than the truncating error. In numerical differentiation of the n-point Lagrangian interpolation polynomial, i.e., p '(x) ~ £j_jL< ^ (x)f(x¡), a criterion for optimal stability is minimization of £*»« \L¡ (x)\. Let L = L(n, k, Xj,..., xn; x or x0)=S^=1l¿¿ '(x or x0)|. For x, and fixed x = Xq

doi:10.1090/s0025-5718-1974-0368391-0
fatcat:r5pshnh67refnlytoltichod7a