Most existing quasi-Newton methods for nonlinear least squares problems incorporate both linear and nonlinear information in the secant update. These methods exhibit good theoretical properties, but are not especially accurate in practice. The objective of this paper is to propose quasi-Newton methods that only update the nonlinearities. We show two advantages of such updates. First, fast conve...

A function based nonlinear least squares estimation (FNLSE) method is proposed and investigated in parameter estimation of Jelinski–Moranda software reliability model. FNLSE extends the potential fitting functions of traditional least squares estimation (LSE), and takes the logarithm transformed nonlinear least squares estimation (LogLSE) as a special case. A novel power transformation function...

Digital super resolution is a term used to describe the inverse problem of reconstructing a high resolution image from a set of known low resolution images, each of which is shifted by subpixel displacements. Simple models assume the subpixel displacements are known, but if the displacements are not known, then nonlinear approaches must be used to jointly find the displacements and the reconstr...

This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton–Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton– Raphson algorithm is robust and ...

This paper considers the issue of parameter estimation for biomedical applications using nonuniformly sampled data. The generalized linear least squares (GLLS) algorithm, first introduced by Feng and Ho (1993), is used in the medical imaging community for removal of bias when the data defining the model are correlated. GLLS provides an efficient iterative linear algorithm for the solution of th...

In this paper, we consider the least squares semidefinite programming with a large number of equality and inequality constraints. One difficulty in finding an efficient method for solving this problem is due to the presence of the inequality constraints. In this paper, we propose to overcome this difficulty by reformulating the problem as a system of semismooth equations with two level metric p...

Blur in images can be removed by solving a series of box-constrained least-squares problems. In this paper, we compare two recent approaches for solving these problems using affine-scaling methods. Both approaches aim at solving a nonlinear system arising from the Karush-Kuhn-Tucker condition. One approach is to identify the active set and update the inactive components of the iterates by using...

We introduce an inexact Gauss-Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties.