In this work, we investigate the ill-conditioned problem of a separable, nonlinear least squares model by using variable projection method. Based on truncated singular value decomposition method and Tikhonov regularization method, propose an improved which neither discards small values, nor treats all corrections. By fitting Mackey–Glass time series in exponential model, compare three methods, ...

Entanglement is an amazing feature of quantum mechanics which is a nontrivial non-local correlation between states. It is studied and exploited greatly in the field of quantum information. Traditionally, most quantum systems of interest in quantum information is described by discrete variable states, e.g. spin of particles. Thus, entanglement is studied to a considerable extent in such state. N...

In this paper, we investigate an inverse problem to determine an unknown source term that has a separable-variable form in the time-fractional diffusion equation, whereby the data is obtained at a certain time. This problem is ill-posed, and we use the Landweber iterative regularization method to solve this inverse source problem. Two kinds of convergence rates are obtained by using an a priori...

We consider the parallel variable distribution (PVD) approach proposed by Ferris and Mangasarian [SIAM J. Optim., 4 (1994), pp. 815–832] for solving optimization problems. The problem variables are distributed among p processors with each processor having the primary responsibility for updating its block of variables while allowing the remaining “secondary” variables to change in a restricted f...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 2 March 2021Accepted: 07 July 2021Published online: 11 November 2021Keywordsinexact Krylov methods, separable nonlinear inverse problems, variable projection method, Tikhonov regularization, image deblurring, blind deblurringAMS Subject Headings65F20, 65F22, 65F30Publicat...

This paper considers an efficient iterative approach to solve separable nonlinear least squares problems that arise in large scale inverse problems. A variable projection GaussNewton method is used to solve the nonlinear least squares problem, and Tikhonov regularization is incorporated using an iterative Lanczos hybrid scheme. Regularization parameters are chosen automatically using a weighted...