Fast Function Extraction (FFX) is a deterministic algorithm for solving symbolic regression problems. We improve the accuracy of FFX by adding parameters to arguments nonlinear functions. Instead only optimizing linear parameters, we optimize these additional with separable least squared optimization using variable projection algorithm. Both and our new applied on PennML benchmark suite. show t...

We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on discrepancy principle. formulate problem as an equality constrained optimization problem, where constraint is given by least squares data fidelity term and expresses The objective function convex that incorporates some prior knowledge, such total variation function. Using Jac...

This paper presents a novel approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint throughput is particularly suitable when the and/or controller parameters change at runtime. The contributions of include: (i) formulation MPC problem as bounded-variable least-squares (BVNLS) problem, demonstrating use an appropriate solver can outperf...

This paper is concerned with the development of a new method for the design of Energy Transfer Filters (ETFs). ETFs are a new class of nonlinear filters recently proposed by the authors, which employ nonlinear effects to transfer signal energy from one frequency band to a different frequency location. The new method uses the powerful Orthogonal Least Squares (OLS) algorithm to solve the Least S...

This contribution gives a brief overview on nonlinear constrained least squares methods. The focus is on data fitting problems in which the models include ordinary or partial differential equations.

Methods are proposed for separation of harmonic sound sources using sinusoidal modeling. A local nonlinear least-squares (NLS) frequency estimator is proposed to resolve sinusoids that are close in frequency. An iterative analysis scheme using interpolated parameter trajectories and subtraction of detected components is presented. A measure is proposed for testing the accuracy of the model.

We use U.S. county data (3,058 observations) and 41 conditioning variables to study growth and convergence. Using ordinary least squares (OLS) and three-stage least squares with instrumental variables (3SLS-IV), we report on the full sample and metro, nonmetro, and and regional samples: (1) OLS yields convergence rates around 2%; 3SLS yields 6%–8%; (2) convergence rates vary (for example, the S...

A nonlinear regression model with correlated, normally distributed errors is investigated. The bias and the mean square error matrix of the approximate least squares estimator of regression parameters are derived and their limit properties are studied.