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Prove that the sequence 1 f(1n) j(zn) 2 f(In) F(x,) ' f(r,) 1 with Xn+1 = n an = %3D an is cubically convergent to a root of f under some conditions.

Prove that the sequence 1 f(1n) j(zn) 2 f(In) F(x,) ' f(r,) 1 with Xn+1 = n an = %3D an is cubically convergent to a root of f under some conditions.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove that the sequence 1. Xn+1 = In (n) 1 f(2,) F(2n) 2 f(r,) with an = an is cubically convergent to a root of f under some conditions.
Transcribed Image Text:Prove that the sequence 1. Xn+1 = In (n) 1 f(2,) F(2n) 2 f(r,) with an = an is cubically convergent to a root of f under some conditions.
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