### Update Newton_s_method_for_systems_of_equations_assignment__with_solutions_.ipynb

parent 82894b65
 %% Cell type:markdown id: tags: # Newton's method for systems of equations Newton's method is used to solve a *general* system of equations, written in vector form $$\mathbf{f}(\mathbf{x}) = \mathbf{0}$$ Given an initial guess $\mathbf{x}_{0}$, Newton's method is used to compute successively better approximations to the solution of the above equation by the following iterative formula $$\mathbf{x}_{k+1} =\mathbf{x}_{k} + \mathbf{f}'(\mathbf{x_k})^{-1}\mathbf{f}(\mathbf{x_k}),$$ $$\mathbf{x}_{k+1} =\mathbf{x}_{k} - \mathbf{f}'(\mathbf{x_k})^{-1}\mathbf{f}(\mathbf{x_k}),$$ where the Jacobain derivative is $$\mathbf{f}'(\mathbf{x}) = \left(\begin{array}{cc} \frac{\partial f_{0}}{\partial x_0} & \frac{\partial f_{0}}{\partial x_1} \\ \frac{\partial f_{1}}{\partial x_0} & \frac{\partial f_{1}}{\partial x_1} \\ \end{array}\right).$$ Your stopping condition should be \$\|\mathbf{f}(\mathbf(x_k))\|
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