Search results for "Linear least squares"
showing 10 items of 11 documents
Algorithms for rational discrete least squares approximation
1975
In this paper an algorithm for the computation of a locally optimal polefree solution to the discrete rational least squares problem under a mild regularity condition is presented. It is based on an adaptation of projection methods [8], [12], [13], [14], [18], [19] to the modified Gaus-Newton method [4], [10]. A special device makes possible the direct handling of the infinitely many linear constraints present in this problem.
Algorithms for Rational Discrete Least Squares Approximation Part I: Unconstrained Optimization
1976
In this paper a modification of L. Wittmeyer’s method ([1], [14]) for rational discrete least squares approximation is given which corrects for its failure to converge to a non-optimal point in general. The modification makes necessary very little additional computing effort only. It is analysed thoroughly with respect to its conditions for convergence and its numerical properties. A suitable implementation is shown to be benign in the sense of F. L. Bauer [2]. The algorithm has proven successful even in adverse situations.
Quantile regression via iterative least squares computations
2012
We present an estimating framework for quantile regression where the usual L 1-norm objective function is replaced by its smooth parametric approximation. An exact path-following algorithm is derived, leading to the well-known ‘basic’ solutions interpolating exactly a number of observations equal to the number of parameters being estimated. We discuss briefly possible practical implications of the proposed approach, such as early stopping for large data sets, confidence intervals, and additional topics for future research.
A generalization of the orthogonal regression technique for life cycle inventory
2012
Life cycle assessment (LCA) is a method used to quantify the environmental impacts of a product, process, or service across its whole life cycle. One of the problems occurring when the system at hand involves processes delivering more than one valuable output is the apportionment of resource consumption and environmental burdens in the correct proportion amongst the products. The mathematical formulation of the problem is represented by the solution of an over-determined system of linear equations. The paper describes the application of an iterative algorithm for the implementation of least square regression to solve this over-determined system directly in its rectangular form. The applied …
Photoluminescence study of terbium-exchanged ultrastable Y zeolites: Number of species, photoluminescence decays and decay-associated spectra
2008
Terbium-exchanged ultrastable Y (USY) zeolites were investigated by using time-resolved photoluminescence spectroscopy techniques and methods. To determine the distribution of terbium species in USY zeolites together with their photoluminescence properties, several analysis methods for the time-resolved luminescence spectra were used such as the area normalization of time-resolved photoluminescence spectra, singular value decomposition, global nonlinear least squares, and the maximum entropy. Except for a questionable long lifetime, small contribution of a terbium species with lifetime of 1.9¿2.1 ms, all the experimental and analysis results converged to a two terbium species distribution w…
TOWARD A SOLUTION OF ALLOCATION IN LIFE CYCLE INVENTORIES: THE USE OF LEAST SQUARES TECHNIQUES
2010
Purpose: The matrix method for the solution of the so-called inventory problem in LCA generally determines the inventory vector related to a specific system of processes by solving a system of linear equations. The paper proposes a new approach to deal with systems characterized by a rectangular (and thus non-invertible) coefficients matrix. The approach, based on the application of regression techniques, allows solving the system without using computational expedients such as the allocation procedure. Methods: The regression techniques used in the paper are (besides the ordinary least squares, OLS) total least squares (TLS) and data least squares (DLS). In this paper, the authors present t…
A modified least squares FE-method for ideal fluid flow problems
1982
A modified least squares FE-method suitable e.g. for calculating the ideal fluid flow is presented. It turns out to be essentially more efficient than the conventional least squares method. peerReviewed
Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring
2013
We introduce a new iterative scheme for solving linear ill-posed problems, similar to nonstationary iterated Tikhonov regularization, but with an approximation of the underlying operator to be used for the Tikhonov equations. For image deblurring problems, such an approximation can be a discrete deconvolution that operates entirely in the Fourier domain. We provide a theoretical analysis of the new scheme, using regularization parameters that are chosen by a certain adaptive strategy. The numerical performance of this method turns out to be superior to state-of-the-art iterative methods, including the conjugate gradient iteration for the normal equation, with and without additional precondi…
Impact of the terrestrial reference frame on the determination of the celestial reference frame.
2022
Currently three up-to-date Terrestrial Reference Frames (TRF) are available, the ITRF2014 from IGN, the DTRF2014 from DGFI-TUM, and JTRF2014 from JPL. All use the identical input data of space-geodetic station positions and Earth orientation parameters, but the concept of combining these data is fundamentally different. The IGN approach is based on the combination of technique solutions, while the DGFI is combining the normal equation systems. Both yield in reference epoch coordinates and velocities for a global set of stations. JPL uses a Kalman filter approach, realizing a TRF through weekly time series of geocentric coordinates. As the determination of the CRF is not independent of the T…
Maximum Likelihood Estimation and non-linear least squares fitting with Levenberg-Marquardt Algorithm implementation in FPGA devices for high resolut…
2012
This work compares two possible solutions to achieve a higher resolution in a hodoscope based on Plastic Scintillating Fibers (PSF) by obtaining the point of maximum incidence of the radioactive beam. The two fitting algorithms proposed have been tested and implemented in Field Programmable Gate Array (FPGA) devices. On one hand, a probabilistic model based on the Maximum Likelihood Estimation (MLE) and on the other hand, non-linear least-squares fit with the Levenberg-Marquardt Algorithm (LMA).