Note that Theorem 4.3 is a because is fixed, a nonlocal convergence theorem s known interval is assumed, and convergence is for any . I Proof: (convergence) Recall that is unique. For any between and s n, xn-1 s such that . Repeating this gives . Since , . Error bound: Note that Since , . QED
Note that Theorem 4.3 is a nonlocal convergence theorem because s is fixed, a known interval I is assumed, and convergence is for any . Proof: (convergence) Recall that s is unique. For any n, between xn-1 and s such that . Repeating this gives . Since , . Error bound: Note that Since , . QED
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