Question

Determine the roots of the following simultaneous nonlinear equations using multiple-equation Newton Raphson method. Carry out two iterations with initial guesses of

x₁⁽⁰⁾ =0.6 and x₂⁽⁰⁾ =1.2. Calculate the approximate relative error ε_a in each iteration by using maximum magnitude norm (║x║∞).

x₁ + 1 - x₂² = 0

x₁² + x₂² – 5 = 0

Answer 1

Answer:

The Newton-Raphson method (also known as Newton's method) is a way to quickly find a good approximation for the root of a real-valued function f ( x ) = 0 f(x) = 0 f(x)=0. It uses the idea that a continuous and differentiable function can be approximated by a straight line tangent to it.