# Linear and Quadratic Taylor ExpansionsΒΆ

The approximation of the model response
around a specific set
of input
parameters may be of interest. One may then substitute for
its Taylor expansion at point . Hence
is replaced with a first or second-order polynomial
whose evaluation is inexpensive, allowing the
analyst to apply the uncertainty propagation methods.

We consider the first and second order Taylor expansions around
.

Introducing a vector notation, the previous equation rewrites:

where:

- is the vector model response evaluated at ;
- is the current set of input parameters;
- is the transposed Jacobian matrix evaluated at .

Introducing a vector notation, the previous equation rewrites:

where is the transposed Hessian matrix.

API:

- See
`LinearTaylor`

- See
`QuadraticTaylor`

Examples: