Numerical Analysis: Difference between revisions
(Created page with "Numerical Analysis ==Nonlinear Equations== ===Continuation/Homotopy Methods=== Reference Numerical Optimization by Nocedal and Wright (2006)<br> Also known as zero-path follo...") |
No edit summary |
||
| Line 5: | Line 5: | ||
Reference Numerical Optimization by Nocedal and Wright (2006)<br> | Reference Numerical Optimization by Nocedal and Wright (2006)<br> | ||
Also known as zero-path following.<br> | Also known as zero-path following.<br> | ||
If you want to solve <math>r(x)=0</math> when <math>r(x)</math> is difficult (i.e. has non-singular Jacobian) then you can use this method. | If you want to solve <math>r(x)=0</math> when <math>r(x)</math> is difficult (i.e. has non-singular Jacobian) then you can use this method.<br> | ||
Define the Homotopy map <math>H(x, \lambda) = \lambda r (x) + (1 | Define the Homotopy map<br> | ||
<math>H(x, \lambda)=\lambda r(x) + (1-\lambda)(x-a)</math> | |||
Revision as of 13:51, 19 October 2019
Numerical Analysis
Nonlinear Equations
Continuation/Homotopy Methods
Reference Numerical Optimization by Nocedal and Wright (2006)
Also known as zero-path following.
If you want to solve \(\displaystyle r(x)=0\) when \(\displaystyle r(x)\) is difficult (i.e. has non-singular Jacobian) then you can use this method.
Define the Homotopy map
\(\displaystyle H(x, \lambda)=\lambda r(x) + (1-\lambda)(x-a)\)