Solved: Apply Newton's method (60 accuracy). First sketch the function(s) to see what is
Chapter 19, Problem 19.1.36(choose chapter or problem)
Apply Newton's method (6D accuracy). First sketch the function(s) to see what is going on.
(Legendre polynomials) Find the largest root of the Legendre polynomial \(P_{5}(x)\) given by \(P_{5}(x)=\frac{1}{8}\left(63 x^{5}-70 x^{3}+15 x\right)\) (Sec. 5.3) (to be needed in Gauss integration in Sec. 19.5) (a) by Newton's method. (b) from a quadratic equation.
Text Transcription:
P_5(x)
P_5(x) = 1 / 8 (63x^5 - 70x^3 + 15x)
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