scholarly journals The power mean and the least squares mean of probability measures on the space of positive definite matrices

2015 ◽  
Vol 465 ◽  
pp. 325-346 ◽  
Author(s):  
Sejong Kim ◽  
Hosoo Lee
Keyword(s):  
Least Squares ◽  
Positive Definite ◽  
Probability Measures ◽  
Power Mean ◽  
Positive Definite Matrices

scholarly journals Least-squares fitting applied to nuclear mass formulas. Solution by the Gauss–Seidel method

2021 ◽  
Author(s):  
B. Mohammed-Azizi ◽  
H. Mouloudj
Keyword(s):  
Linear System ◽  
Least Squares ◽  
Statistical Data ◽  
Large Data ◽  
Positive Definite ◽  
Nuclear Mass ◽  
Positive Definite Matrices ◽  
Seidel Method ◽  
Semi Empirical ◽  
Mass Formulas

In this paper, a numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear system which is solved by iterations according to the Gauss–Seidel scheme. The steps of the algorithm are given in detail. In practice, the method is very simple to implement and is able to treat large data in a very fast way. In fact, although this method has been illustrated here by specific examples, it can be applied without difficulty to any experimental or statistical data of the same type, i.e. those leading to linear system characterized by symmetric and positive-definite matrices.

The quasi-arithmetic means and Cartan barycenters of compactly supported measures

2018 ◽  
Vol 30 (3) ◽  
pp. 753-765
Author(s):  
Sejong Kim
Keyword(s):  
Positive Definite ◽  
Probability Measures ◽  
Central Tendency ◽  
Hermitian Matrices ◽  
Research Topics ◽  
Positive Definite Matrices ◽  
Arithmetic Means ◽  
Power Means ◽  
Computational Research ◽  
Important Notion

AbstractSince positive definite Hermitian matrices have become fundamental objects in many areas, a variety of theoretical and computational research topics have been arisen. Especially, the average of positive definite matrices is a very important notion to see the central tendency of objects. There are many different kinds of averages for a finite number of positive definite matrices such as quasi-arithmetic means, power means and Cartan barycenters. We generalize these averages to the setting of positive definite matrices equipped with probability measures of compact support, and show the monotonicity of quasi-arithmetic means for parameters {\geq 1}, and connections with inequalities between quasi-arithmetic means and power means, and between quasi-arithmetic means and Cartan barycenters.

scholarly journals Multi-variable weighted geometric means of positive definite matrices

2011 ◽  
Vol 435 (2) ◽  
pp. 307-322 ◽  
Author(s):  
Hosoo Lee ◽  
Yongdo Lim ◽  
Takeaki Yamazaki
Keyword(s):  
Positive Definite ◽  
Positive Definite Matrices ◽  
Geometric Means
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