Consider the Newton-Raphson method for finding root of a nonlinear function ??+1=??−?(??)?′(??), ?≥0. a) Prove that...

Consider the Newton-Raphson method for finding root of a nonlinear function
??+1=??−?(??)?′(??), ?≥0.
a) Prove that if ? is simple zero of ?(?), then the N-R iteration has quadratic convergence.
b) Prove that if ? is zero of multiplicity ? , then the N-R iteration has only linear convergence.

Expert Solution

Colby Messinger answered 2 years ago

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