Newton’s Method for Systems of Nonlinear Equations

Generalized Newton’s method for systems of nonlinear equations. Lesson goes over numerically solving multivariable nonlinear equations step-by-step with visual examples and explanation of the Jacobian, the backslash operator, and the inverse Jacobian. Example code in MATLAB / GNU Octave on GitHub: Chapters 0:00 Intro 0:12 Prerequisites 0:32 Background 0:58 Setup 1:54 Jacobian 2:55 Historical Context 5:11 Newton’s Method Example Step-by-Step 6:57 End Condition 7:12 Numerical Example in Table 7:33 Newton’s Method with Backslash 7:53 Newton’s Method with Inverse Jacobian 8:16 MATLAB / GNU Octave 9:01 Newton Fractals 10:51 3D Fractal 11:37 Historical Optimization Newton’s Method 12:18 Oscar’s Notes 12:59 Thank You Recommended Viewing: Newton’s Method Newton Fractals Newton-Bisection Hybrid