On the L1-Norm Approximation of a Matrix by Another of Lower Rank

Author(s):  
Nicholas Tsagkarakis ◽  
Panos P. Markopoulos ◽  
Dimitris A. Pados
2019 ◽  
Vol 3 (1) ◽  
pp. 11-21
Author(s):  
Bijan Bidabad

In this paper, the L1 norm of continuous functions and corresponding continuous estimation of regression parameters are defined. The continuous L1 norm estimation problem of one and two parameters linear models in the continuous case are solved. We proceed to use the functional form and parameters of the probability distribution function of income to exactly determine the L1 norm approximation of the corresponding Lorenz curve of the statistical population under consideration. Iran family budget data were used to estimate income distribution for the period of 1362-1370.  


2019 ◽  
Vol 1 (1) ◽  
pp. 41-49
Author(s):  
Bijan Bidabad

In this paper, the L1 norm of continuous functions and corresponding continuous estimation of regression parameters are defined. The continuous L1 norm estimation problem of one and two parameters linear models in the continuous case is solved. We proceed to use the functional form and parameters of the probability distribution function of income to exactly determine the L1 norm approximation of the corresponding Lorenz curve of the statistical population under consideration.    


2017 ◽  
pp. 94-108 ◽  
Author(s):  
Yu. A. Semenishchenkov

Phytogeographical features of forest vegetation at the level of lower-rank syntaxa were being discussed in literature since the early 20th century (Cajander, 1903; Sukachev, 1926; Braun-Blanquet, 1964; Kral et al., 1975; Kleopov, 1990; Bulokhov, 2003; Ellenberg, 2009), however, phytocoenologists still have no uniform interpretation and geographical maintenance of lower classification units. Forest vegetation of the European part of Russia is well studied according to Braun-Blanquet approach with association as a system of geographical subassociations. The paper offers the approaches to the reflection of geographical variations of the natural forest vegetation in the basin of the Upper Dnieper (central part of the East European Plain) at the level of lower-rank syntaxa The xeromesophytic oak woods in the basin of the Upper Dnieper belong to the East European ass. Lathyro nigri–Quercetum roboris Bulokhov et Solomeshch 2003. Floristic differentiation of this association from the similar Central European ass. Potentillo-Quercetum is given. These two associations have large blocks of geographically significant differential species that does not allow to consider them as a part of one association. The suggested approach allows to define the chorological content of units of lower syntaxonomical ranks and make regional classification schemes comparable to each other.


2019 ◽  
Author(s):  
Philipp Kremer ◽  
Damian Brzyski ◽  
Malgorzata Bogdan ◽  
Sandra Paterlini
Keyword(s):  

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 65091-65100
Author(s):  
Ayyad Maafiri ◽  
Omar Elharrouss ◽  
Saad Rfifi ◽  
Somaya Ali Al-Maadeed ◽  
Khalid Chougdali

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