# Numerical Analysis


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
$$\displaystyle H(x, \lambda)=\lambda r(x) + (1-\lambda)(x-a)$$

## Numerical Differentiation

See finite differencing