Three-dimensional magnetotelluric inversion using a heterogeneous smoothness-constrained least-squares method

2013 ◽  
Vol 44 (3) ◽  
pp. 145-155 ◽  
Author(s):  
Tateyuki Negi ◽  
Hideki Mizunaga ◽  
Koichi Asamori ◽  
Koji Umeda
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Constrained Least Squares ◽  
Magnetotelluric Inversion

Structure cristalline et moléculaire du cyclopentadiényle dicarbonyle triphénylphosphine manganèse, MnC5H5(CO)2P(C6H5)3

1973 ◽  
Vol 51 (18) ◽  
pp. 3027-3031 ◽  
Author(s):  
Claude Barbeau ◽  
Klaus Sorrento Dichmann ◽  
Louis Ricard
Keyword(s):  
Molecular Structure ◽  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Triphenyl Phosphine ◽  
Triclinic Space Group ◽  
Space Group ◽  
Bond Lengths ◽  
Atomic Parameter

The crystalano molecular structure of cyclopentadienyl manganese dicarbonyl-triphenyl phosphine has been determined by means of three dimensional data obtained by a Buerger precession camera. 2931 independent intensities were utilized in the refinement of the structure using the least-squares method. The final disagreement factor is 0.11. MnC5H5(CO)2P(C6H5)3 crystallizes in the triclinic space group.[Formula: see text]The molecule shows atomic parameter almost identical to those of MnC5H5(CO)3 except for the Mn—C bond lengths which change from 1.80 to 1.73 Å. The Mn—P distance (2.236 Å) and the unchanged parameters for the Mn—C5H5 group confirm the strong donating power of the cyclopentadienyl group. [Journal translation]

scholarly journals Three-dimensional GPS ionospheric tomography over Japan using constrained least squares

2014 ◽  
Vol 119 (4) ◽  
pp. 3044-3052 ◽  
Author(s):  
Gopi K. Seemala ◽  
Mamoru Yamamoto ◽  
Akinori Saito ◽  
Chia-Hung Chen
Keyword(s):  
Least Squares ◽  
Three Dimensional ◽  
Constrained Least Squares ◽  
Ionospheric Tomography

A Three-Dimensional Generalization of Reuleaux’s Method Based on Line Geometry

2006 ◽  
Author(s):  
Jasem Baroon ◽  
Bahram Ravani
Keyword(s):  
Rigid Body ◽  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Line Geometry ◽  
Basic Form ◽  
Motion Reconstruction ◽  
Linear Solution ◽  
On Line

In kinematics, the problem of motion reconstruction involves generation of a motion from the specification of distinct positions of a rigid body. In its most basic form, this problem involves determination of a screw displacement that would move a rigid body from one position to the next. Much if not all of the previous work in this area has been based on point geometry. In this paper, we develop a method for motion reconstruction based on line geometry. An elegant geometric method is developed based on line geometry that can be considered as a generalization of the classical Reuleaux’s method used in 2D kinematics. The case of over determined system is also considered a linear solution is presented based on least squares method.

N-way partial least squares combined with new self-construction strategy—A promising approach of using near infrared spectral data for quantitative determination of multiple compounds

2019 ◽  
Vol 28 (2) ◽  
pp. 113-121
Author(s):  
Xiang-Zhi Zhang ◽  
Ai-Jun Ma ◽  
Na Feng ◽  
Bao Qiong Li
Keyword(s):  
Quantitative Analysis ◽  
Least Squares ◽  
Partial Least Squares ◽  
Near Infrared ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Near Infrared Spectra ◽  
Infrared Spectral ◽  
Construction Strategy ◽  
Partial Least Squares Method

Because of the complexity of near infrared spectral data, effective strategies are necessary proposed for accurate quantitative analysis purpose. This work explores a new self-construction strategy for the arrangement of conventional near infrared two-dimensional spectra into new self-constructed three-dimensional spectra, and investigate the feasibility of N-way partial least squares combined with the new self-constructed three-dimensional near infrared spectra for obtaining accurate quantitative determination results. A proof-of-concept model system, the quantitative analysis of four components (moisture, oil, protein, and starch) in corn samples, was applied to evaluate the performance of the proposed strategy. The ability of the newly proposed approach to predict the target compounds was checked with test samples. The established models have good predictive power for the target compounds with acceptable values of Rp (range from 0.82 to 0.997) and RMSEP (range from 0.03 to 0.47). Compared with partial least squares method on pretreated near infrared spectra and N-way partial least squares method on the basis of near infrared self-constructed three-dimensional spectra, the proposed method is competitive.

Total Least-Squares Methods for Active View Registration of Three-Dimensional Line Laser Scanning Data

2004 ◽  
Vol 127 (1) ◽  
pp. 50-56 ◽  
Author(s):  
F. Xi ◽  
D. Nancoo ◽  
G. Knopf
Keyword(s):  
Least Squares ◽  
Laser Scanning ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Measurement Data ◽  
Ordinary Least Squares ◽  
Total Least Squares ◽  
Position Measurement ◽  
Point Position ◽  
Ordinary Least Squares Method

In this paper a method is proposed to register three-dimensional line laser scanning data acquired in two different viewpoints. The proposed method is based on three-point position measurement by scanning three reference balls to determine the transformation between two views. Since there are errors in laser scanning data and sphere fitting, the two sets of three-point position measurement data at two different views are both subject to errors. For this reason, total least-squares methods are applied to determine the transformation, because they take into consideration the errors both at inputs and outputs. Simulations and experiment are carried to compare three methods, namely, ordinary least-squares method, unconstrained total least-squares method, and constrained total least-squares method. It is found that the last method gives the most accurate results.

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