  Parameter-dependent models arise in many contexts such as uncertainty
quantification, sensitivity analysis, inverse problems or optimization.
Parametric or uncertainty analyses usually require the evaluation of an output
of a model for many instances of the input parameters, which may be intractable
for complex numerical models. A possible remedy consists in replacing the model
by an approximate model with reduced complexity (a so called reduced order
model) allowing a fast evaluation of output variables of interest. This chapter
provides an overview of low-rank methods for the approximation of functions
that are identified either with order-two tensors (for vector-valued functions)
or higher-order tensors (for multivariate functions). Different approaches are
presented for the computation of low-rank approximations, either based on
samples of the function or on the equations that are satisfied by the function,
the latter approaches including projection-based model order reduction methods.
For multivariate functions, different notions of ranks and the corresponding
low-rank approximation formats are introduced.

Numerical Analysis