Chapter Four. Matrix Means

2009 ◽  
pp. 101-140
Keyword(s):  
Matrix Means

scholarly journals D-Optimal Slope Design for Second Degree Kronecker Model Mixture Experiment With Three Ingredients

2020 ◽  
Vol 9 (2) ◽  
pp. 30
Author(s):  
Ngigi Peter Kung’u ◽  
J. K. Arap Koske ◽  
Josphat K. Kinyanjui
Keyword(s):  
Information Matrix ◽  
Coefficient Matrix ◽  
Three Dimensions ◽  
Matrix Means ◽  
The Matrix ◽  
Optimal Values ◽  
The Moment ◽  
Product Algebra ◽  
Slope Design ◽  
Second Degree

This study presents an investigation of an optimal slope design in the second degree Kronecker model for mixture experiments in three dimensions. The study is restricted to weighted centroid designs, with the second degree Kronecker model. A well-defined coefficient matrix is used to select a maximal parameter subsystem for the model since its full parameter space is inestimable. The information matrix of the design is obtained using a linear function of the moment matrices for the centroids and directly linked to the slope matrix. The discussion is based on Kronecker product algebra which clearly reflects the symmetries of the simplex experimental region. Eventually the matrix means are used in determining optimal values of the efficient developed design.

On some inequalities with matrix means

2015 ◽  
Vol 63 (12) ◽  
pp. 2373-2378 ◽  
Author(s):  
Xiaohui Fu ◽  
Dinh Trung Hoa
Keyword(s):  
Matrix Means

Some geometric properties of matrix means with respect to different metrics

Positivity ◽  
2020 ◽  
Vol 24 (5) ◽  
pp. 1419-1434
Author(s):  
Trung Hoa Dinh ◽  
Raluca Dumitru ◽  
Jose A. Franco
Keyword(s):  
Geometric Properties ◽  
Matrix Means

scholarly journals On Pointwise Approximation of Conjugate Functions by Some Hump Matrix Means of Conjugate Fourier Series

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
W. Łenski ◽  
B. Szal
Keyword(s):  
Fourier Series ◽  
Conjugate Functions ◽  
Pointwise Approximation ◽  
Conjugate Fourier Series ◽  
Summability Methods ◽  
Matrix Means ◽  
Special Cases ◽  
Norm Approximation

The results generalizing some theorems onN, pnE, γsummability are shown. The same degrees of pointwise approximation as in earlier papers by weaker assumptions on considered functions and examined summability methods are obtained. From presented pointwise results, the estimation on norm approximation is derived. Some special cases as corollaries are also formulated.

scholarly journals On the Approximation of Functions From Lp by Some Special Matrix Means of Fourier Series

2015 ◽  
Vol 55 (1) ◽  
pp. 81-90
Author(s):  
Radosława Kranz ◽  
Aleksandra Rzepka
Keyword(s):  
Fourier Series ◽  
Pointwise Approximation ◽  
Approximation Of Functions ◽  
Summability Methods ◽  
Matrix Means ◽  
Special Cases ◽  
Special Matrix ◽  
Norm Approximation ◽  
Appl Math

Abstract The results corresponding to some theorems of S. Lal [Appl. Math. and Comput. 209 (2009), 346-350] and the results of W. Łenski and B. Szal [Banach Center Publ., 95, (2011), 339-351] are shown. The better degrees of pointwise approximation than these in mentioned papers by another assumptions on summability methods for considered functions are obtained. From presented pointwise results the estimation on norm approximation are derived. Some special cases as corollaries are also formulated.

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