Fast high‐resolution Radon transforms by greedy least‐squares method

2009 ◽  
Author(s):  
Juefu Wang ◽  
Mark Ng ◽  
Mike Perz
Keyword(s):  
High Resolution ◽  
Least Squares ◽  
Least Squares Method ◽  
Radon Transforms

Rotational analysis of the B2Σ+ – A2Πi system of the 12C16O+ molecule

1987 ◽  
Vol 65 (1) ◽  
pp. 94-100 ◽  
Author(s):  
Z. Jakubek ◽  
R. Kepa ◽  
A. Para ◽  
M. Rytel
Keyword(s):  
High Resolution ◽  
Least Squares ◽  
Least Squares Method ◽  
Nonlinear Least Squares ◽  
Spin Rotation ◽  
Spin Orbit ◽  
Rotational Analysis ◽  
Molecular Constants ◽  
Nonlinear Least Squares Method ◽  
First Time

The three bands (0–0, 1–0, 0–1) of the B2Σ+ – A2Πi system of the 12C16O+ molecule have been photographed at high resolution. In total, 824 lines were measured, from which 608 were fitted by a nonlinear least squares method to determine 33 molecular constants. The band-by-band results were merged to obtain 23 molecular constants for the B2Σ+, ν = 0 and 1, and A2Πi, ν = 0 and 1, states. The Λ-doubling constants and spin-orbit constants in the A2Πi, ν = 1 state and spin-rotation constants in the B2Σ+, ν = 0 and 1 states were obtained for the first time, and other constants were defined more precisely.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

Sign in / Sign up

Export Citation Format

Share Document