5_System of Nonlinear Equations

# 5_System of Nonlinear Equations - System of Nonlinear...

This preview shows pages 1–7. Sign up to view the full content.

System of Nonlinear Equations

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Consider the n - dimensional version of solving a single equation f(x) = 0 Statement of the problem n simultaneous nonlinear equations to be solved
The simplest and easiest method is Newton – Raphson Method Need a good starting point Variants of this method have good convergence properties

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Taylor series expansion of about point x By dropping the higher order terms J(x) is the Jacobian matrix (n×n) made up of the partial derivatives Linear approximation of the vector valued function f in the vicinity of x
Assume x as the current approximate solution of f(x) = 0 Let ° + ∆° be an improved solution To find the correction ∆± put ² ± + ∆± = 0 Result a set of linear equations for ∆± ³ ° ∆° = −´(°) Solve for the increments and improve the solution

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Steps in Newton – Raphson Method Estimate the solution vector x Evaluate f(x) Compute the Jacobian matrix J(x)
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern