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= Let ƒ € Cm+¹ and the multiplicity of the root x* of f be n. In other words, f(x*) = ƒ'(x*) = = f(n−¹)(x*) = 0 and ƒ(¹)(x*) ‡ 0. We want to find the root x* using the modified Newton's method: == f(xk) f'(xk) Determine μl for which convergence is guaranteed to be quadratic. £k+1= k — |- .

= Let ƒ € Cm+¹ and the multiplicity of the root x* of f be n. In other words, f(x*) = ƒ'(x*) = = f(n−¹)(x*) = 0 and ƒ(¹)(x*) ‡ 0. We want to find the root x* using the modified Newton's method: == f(xk) f'(xk) Determine μl for which convergence is guaranteed to be quadratic. £k+1= k — |- .

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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= Let ƒ € C+¹ and the multiplicity of the root x* of ƒ be n. In other words, ƒ(x*) = f(n−¹) (x*) = 0 and f(n)(x*) ‡ 0. We want to find the root x* using the = ... = ƒ'(x*) modified Newton's method: f(xk) μl 'f'(xk)* Determine μ for which convergence is guaranteed to be quadratic. k+1= k
Transcribed Image Text:= Let ƒ € C+¹ and the multiplicity of the root x* of ƒ be n. In other words, ƒ(x*) = f(n−¹) (x*) = 0 and f(n)(x*) ‡ 0. We want to find the root x* using the = ... = ƒ'(x*) modified Newton's method: f(xk) μl 'f'(xk)* Determine μ for which convergence is guaranteed to be quadratic. k+1= k
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