In this paper, we introduce adaptive network enhancement (ANE) method for the best least-squares approximation using two-layer ReLU neural networks (NNs). For a given function f(x), ANE generates NN and numerical integration mesh such that accuracy is within prescribed tolerance. The provides natural process obtaining good initialization which crucial training nonlinear optimization problems. N...

One of the most commonly used methods for the analysis of experimental data in the biochemical literature is nonlinear least squares (regression). This group of methods are also commonly misused. The purpose of this article is to review the assumptions inherent in the use of least-squares techniques and how these assumptions govern the ways that least-squares techniques can and should be used. ...

This paper presents a new approach to shaping of the frequency response of the sensitivity function. A sensitivity shaping problem is formulated as an approximation problem relative to a desired frequency response and with respect to a function in a class of sensitivity functions with a degree bound. It is reduced to a finite dimensional constrained nonlinear least-squares optimization problem....

Attitude determination is a popular application of Global Navigation Satellite Systems (GNSS). Many methods have been developed to solve the attitude problem with different performance offerings. We develop constrained wrapped least-squares (C-WLS) method for highaccuracy determination. This approach built on an optimization model that leverages prior information related antenna array and integ...

The mathematical problem of approximating one matrix by another of lower rank is closely related to the fundamental postulate of factor-theory. When formulated as a least-squares problem, the normal equations cannot be immediately written do~vn, since the elements of the approximate matrix are not independent of one another. The solution of the problem is simplified by first expressing the matr...