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2. a) Write down Newton's method for approximating the square root of a positive number c.

2. a) Write down Newton's method for approximating the square root of a positive number c.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. a) Write down Newton's method for approximating the square root of a positive number c. b) Find a simple recursion relation for the error en = xn- - √c. c) Prove, using the recursion form part (b), that i) If xo > √c, the sequence n will monotonically decrease to √c. ii) The convergence will be quadratic as the limit is approached. d) Describe what happens to the sequence of iterates if we start with an arbitrary initial value xo(either positive or negative).
Transcribed Image Text:2. a) Write down Newton's method for approximating the square root of a positive number c. b) Find a simple recursion relation for the error en = xn- - √c. c) Prove, using the recursion form part (b), that i) If xo > √c, the sequence n will monotonically decrease to √c. ii) The convergence will be quadratic as the limit is approached. d) Describe what happens to the sequence of iterates if we start with an arbitrary initial value xo(either positive or negative).
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