In this paper we review 30 years of developments and applications of the variable projection
method for solving separable nonlinear least-squares problems. These are problems for …

For a class of nonlinear least squares problems, it is usually very beneficial to separate the
variables into a linear and a nonlinear part and take full advantage of reliable linear least …

The Levenberg-Marquardt algorithm is often superior to other training algorithms in off-line
applications. This motivates the proposal of using a recursive version of the algorithm for on …

In this article, we study the recursive algorithms for a class of separable nonlinear models
(SNLMs) in which the parameters can be partitioned into a linear part and a nonlinear part …

Broken rotor bars in induction motors can be detected by monitoring any abnormality of the
spectrum amplitudes at certain frequencies in the motor-current spectrum. It has been shown …

The radial basis function network-based autoregressive with exogenous inputs (RBF-ARX)
models have much more linear parameters than nonlinear parameters. Taking advantage of …

The Hammerstein cascade, consisting of a zero-memory nonlinearity followed by a linear
filter, is often used to model nonlinear biological systems. This structure can represent some …

Separable nonlinear models are very common in various research fields, such as machine
learning and system identification. The variable projection (VP) approach is efficient for the …

We present a method for computing the inverse parameters and the solution field to inverse
parametric partial differential equations (PDE) based on randomized neural networks. This …

This paper considers the use of cubic splines, instead of polynomials, to represent the static
nonlinearities in block structured models. It introduces a system identification algorithm for …