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Use Newton iteration to find: √91, start with xo 10 Xn+1 A Xn+ ( = `xn' 2

Use Newton iteration to find: √91, start with xo 10 Xn+1 A Xn+ ( = `xn' 2

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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newton methode with square root

Use Newton iteration to find: √91, start with Xo = 10 Xn+1 Xn+ (A) Χη 2
Transcribed Image Text:Use Newton iteration to find: √91, start with Xo = 10 Xn+1 Xn+ (A) Χη 2
Expert Solution
Step 1: Explanation to Newton's Method

Let us assume that we need to find the square root of n∈N.

Consider,

x=n

x2=n

x2−n=0

Assume f(x)=x2−n. Then f′(x)=2x.

By Newton's Method, we know that

xn+1=xn−f(xn)f′(xn)

xn+1=xn−xn2−n2xn

after solving we get,

xn+1=xn+nxn2

In our problem, n=91. Therefore, formula reduces to

xn+1=xn+91xn2

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