GATE Numerical Analysis: Nonlinear Equations – Previous Year Questions
6 GATE previous year questions on Nonlinear Equations (Numerical Analysis, Mathematics) with answers and explanations, from every paper.
- GATE 2021 MA Q18 – For x (n+1)=φ(x n),φ(x)=3+(x−3)³ on (2.5,3.5), and x₀=3.25, find the convergence order.
- GATE 2021 MA Q31 – For f(x)=x⁴+2x³−11x²−12x+36, Newton iteration from x₀=2.1 finds root α=2. What is its convergence order?
- GATE 2022 MA Q18 – For x n=x (n−1)/2+1/x (n−1),n≥1, which is true?
- GATE 2023 MA Q51 – A twice continuously differentiable f on [a,b] has f′<0,f″<0 on (a,b), and f(ζ)=0 at ζ∈(a,b). Newton iteration is x (k+1)=x k−f(x k)/f′(x k). If x…
- GATE 2024 MA Q52 – Let p₁<p₂ be the two fixed points of g(x)=eˣ−2, and x n=g(x (n−1)). Which statements hold?
- GATE 2025 MA Q13 – For x³+4x²−10=0 in (1,3/2), consider S1: x k+1=10/(4+x k) converges for every initial x₀ in that interval. S2: x k+1=1210-x k3 diverges for some such…