nlstac: Non-Gradient Separable Nonlinear Least Squares Fitting

Abstract

A new package for nonlinear least squares fitting is introduced in this paper. This package implements a recently developed algorithm that, for certain types of nonlinear curve fitting, reduces the number of nonlinear parameters to be fitted. One notable feature of this method is the absence of initialization which is typically necessary for nonlinear fitting gradient-based algorithms. Instead, just some bounds for the nonlinear parameters are required. Even though convergence for this method is guaranteed for exponential decay using the max-norm, the algorithm exhibits remarkable robustness, and its use has been extended to a wide range of functions using the Euclidean norm. Furthermore, this data-fitting package can also serve as a valuable resource for providing accurate initial parameters to other algorithms that rely on them.

Figures (8)

• Figure 1: Schematic workflow of the algorithm used in the nlstac package.
• Figure 2: Example 1. Fitting an exponential decay for CoolingWater dataset. The figure shows the original data (grey points) and the nlstac fit along with the nls fit (green line).
• Figure 3: Example 2. Fit of a bi-exponential decay for data of subject 3 in Indometh dataset. The figure shows the original data (grey points), the nlstac fit (green line) and the nls fit (red line)
• Figure 4: Example 3. The combined trend of three exponential decays with phase displacement. The figure shows the original data (grey points), the nlstac fit (green line) and the nls fit using nlstac's best approximation (red line).
• Figure 5: Example 4. Fit of an exponential decay mixed with a sinusoidal signal for dataset considered in example 4 with the model given in \ref{['eq:pattern_exp_sin']}. The figure shows the original data (grey points), the nlstac fit (green line), the nls fit initialized with nlstac output (red line) and the nls fit initialized with a vector of ones (blue line).