A Method for Separable Nonlinear Least Squares Problems with Separable Nonlinear Equality Constraints

An Efficient Algorithm for the Separable Nonlinear Least Squares Problem

The nonlinear least squares problem miny,z‖A(y)z + b(y)‖, where A(y) is a full-rank (N + `)× N matrix, y ∈ Rn, z ∈ RN and b(y) ∈ RN+` with ` ≥ n, can be solved by first solving a reduced problem miny‖ f (y)‖ to find the optimal value y∗ of y, and then solving the resulting linear least squares problem minz‖A(y∗)z + b(y∗)‖ to find the optimal value z∗ of z. We have previously justified the use o...

Separable Nonlinear Least Squares: the Variable Projection Method and its Applications

Algorithms for separable nonlinear least squares with application to modelling time-resolved spectra

The multiexponential analysis problem of fitting kinetic models to timeresolved spectra is often solved using gradient-based algorithms that treat the spectral parameters as conditionally linear. We make a comparison of the two most-applied such algorithms, alternating least squares and variable projection. A numerical study examines computational efficiency and linear approximation standard er...

Identification of Linear Systems with Errors in Variables Using Separable Nonlinear Least-squares

It is well-known that the least-squares identification method generally gives biased parameter estimates when the observed input-output data are corrupted with noise. If the noise acting on both the input and output is white, and if the noise variances are known, or if estimates of the noise variances are available, then the principle of biasedcompensated least-squares (CLS) can readily be used...

Modified Gauss Elimination Technique for Separable Nonlinear Programming Problem