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Prove that the Lagrangian coef?cient polynomials for pn(x) satisfy ∑n k=0 lk(x) = 1.
Hint: It is only a 3-line proof. Consider the interpolating polynomial for a constant function f.
The system has a solution near (-0.5,-0.7). Set up the matrix equation Jδ = -f for Newton's method and then carry out one iteration, starting with x 0 = -0.5, y 0 = -0.7.
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