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GATE 2021 MA – Question 31

Numerical Analysis · Nonlinear Equations · 1 mark · Numerical answer

For f(x)=x⁴+2x³−11x²−12x+36, Newton iteration from x₀=2.1 finds root α=2. What is its convergence order?

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Correct answer: 1 to 1

Explanation

Factor f=(x−2)²(x+3)². The root 2 has multiplicity 2, so unmodified Newton iteration converges linearly, with asymptotic error ratio (2−1)/2=1/2. Order **1**.

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