The Application of Digital Filters to the Analysis of Ge and Si(Li) Detector X-Ray Spectra

1979 ◽  
Vol 23 ◽  
pp. 125-131
Author(s):  
L. A. Rayburn
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Digital Filter ◽  
Digital Filters ◽  
Least Squares Method ◽  
Linear Least Squares ◽  
Raw Data ◽  
X Ray ◽  
Peak Structure

AbstractOne of the uncertain aspects in the analysis of x-ray spectra is the determination of the proper background to subtract from the raw data. In those cases where the background is a smoothly varying funct ion of the x-ray energy, the application of a digital filter to the raw data will effectively remove the background leaving only the filtered peak information. These filtered peaks can then be fit by using a non-linear least squares method in conjunction with a suitably chosen mathematical model of the peak structure.

A least squares method for earthquake mechanism determination using S-wave data

1964 ◽  
Vol 54 (6A) ◽  
pp. 2037-2047
Author(s):  
Agustin Udias
Keyword(s):  
Least Squares ◽  
Statistical Evaluation ◽  
Least Squares Method ◽  
Numerical Approach ◽  
Focal Mechanisms ◽  
Least Square ◽  
S Wave ◽  
Double Couple ◽  
Earthquake Mechanism

abstract In this paper a numerical approach to the determination of focal mechanisms based on the observation of the polarization of the S wave at N stations is presented. Least-square methods are developed for the determination of the orientation of the single and double couple sources. The methods allow a statistical evaluation of the data and of the accuracy of the solutions.

scholarly journals Determination of parameters for Cauchy’s problem for systems of ODEs with application to biological modelling

BIOMATH ◽  
2016 ◽  
Vol 5 (1) ◽  
pp. 1604231
Author(s):  
A.N. Pete ◽  
Peter Mathye ◽  
Igor Fedotov ◽  
Michael Shatalov
Keyword(s):  
Experimental Data ◽  
Mathematical Models ◽  
Least Squares ◽  
Numerical Method ◽  
Least Squares Method ◽  
Algebraic Equations ◽  
Systems Of Odes ◽  
Determination Of Parameters ◽  
Biological Modelling

An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.

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