Question

For the Newton-Raphson method to work, one should make sure that ${\mathbf{J}}^{\mathbf{-}\mathbf{1}}$exists.

(a) True

(b) False

Short answer

Therefore, the correct option is (a) True.

Step-by-step solution

Determine the formula of Newton Raphson equation.

Write the Newton Raphson iterative equation.

$\mathbf{X}\left(i+1\right)\mathbf{=}\mathbf{x}\left(i\right)\mathbf{+}{\mathbf{J}}^{\mathbf{-}\mathbf{1}}\left(i\right)\left\{y-f\left[x\left(i\right)\right]\right\}$

Here, if $x\left(i+1\right)$ is present value then $x\left(i\right)$ is previous value and $J\left(i\right)$ is Jacobianmatrix.

Determine the answer.

To use the Newton Raphson iterative method$J^{-1}\left(i\right)$should exists.

Hence, for the Newton-Raphson method to work, one should make sure that $J^{-1}$ exists.

Therefore, the correct option is (a) True.