Topic
Non-linear least squares
About: Non-linear least squares is a research topic. Over the lifetime, 6667 publications have been published within this topic receiving 273089 citations.
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TL;DR: In this article, the relationship between least squares and maximum likelihood estimation was examined, where the likelihood function is the product of two explicit functions, and showed that this can be estimated by commonly accessible non-linear least squares estimation packages.
01 Jan 2022
TL;DR: An improved version of the derivative-free nonlinear least squares iterative solver developed earlier by the author is described in this paper , where a regularization technique is applied to stabilize the evaluation of search directions similar to the one used in the Levenberg-Marquardt methods.
Abstract: An improved version of derivative-free nonlinear least squares iterative solver developed earlier by the author is described. First, we apply a regularization technique to stabilize the evaluation of search directions similar to the one used in the Levenberg-Marquardt methods. Second, we propose several modified designs for the rectangular preconditioning matrix, in particular a sparse adaptive techniques avoiding the use of pseudorandom sequences. The resulting algorithm is based on easily parallelizable computational kernels such as dense matrix factorizations and elementary vector operations thus having a potential for an efficient implementation on modern high-performance computers. Numerical results are presented for several standard test problems as well as for some special complex-valued cases to demonstrate the effectiveness of the proposed improvements to method.
30 Oct 2009
TL;DR: In this article, the damping OAO was introduced into conventional nonlinear regression analysis, and the numerical experiment results indicate the superior application performance of the damp OAAO.
Abstract: The nonlinear regression analysis (RA) is widely used in signal and image processing, but the ill-conditioning problem and the convergence property of classical nonlinear RAs depend on the initial parameter estimates in a great degree. The orthogonal array optimization (OAO) is one of the approaches to get the initial estimates that are near to the optimal values. We introduced the damping idea into conventional OAO, hereby termed as the damping OAO. This paper presents the numerical method of the damping OAO. The numerical experiment results indicate the superior application performance of the damping OAO. It is well known that the nonlinear regression analysis (RA) is widely used in signal and image processing fields. In statistics, nonlinear RA is a form of RA, where observational data are modeled by a function, which is a nonlinear combination of the model parameters and depends on one or more independent variables. Nonlinear least squares method is the common form of nonlinear RAs. The basis of the method is to approximate the model by a linear one and to refine the unknown parameters by successive iterations; and the initial parameter estimates is highly significant for the ill- conditioning problem and the convergence property of the method (1). There are many approaches to get the initial parameter estimates that are near to the optimal values, one of which is the orthogonal array optimization (OAO) (1-2).
01 Jan 1994
01 Dec 2009
TL;DR: In this article, the improved nonlinear least squares method (INLS), the optimized conditions and characteristics, nonlinear fitting are carried out on poisonous gas concentration data and the fitting formula are deduced Using this formula and the ones in the references, the CO concentration and distribution are analyzed and studied.
Abstract: Predicting the concentration and distribution of poisonous gas in the mixture after gas explosion in roadway is greatly significant to safety management and staff protection Using the improved nonlinear least squares method (INLS), the optimized conditions and characteristics, nonlinear fitting are carried out on poisonous gas concentration data and the fitting formula are deduced Using this formula and the ones in the references, the CO concentration and distribution are analyzed and studied Utilizing the improved nonlinear least squares method and the fitting formula, the CO concentration and distribution are simulated The results show that the fitting formula deduced and in the reference have been made on the more desired results in the application of simulation and comparison It is concluded and proved that the nonlinear least-squares method, the optimization conditions and features and fitting formula are correct in comparison and simulation