Complementary performance analysis of general complex-valued diffusion LMS for noncircular signals

2019 ◽  
Vol 160 ◽  
pp. 237-246 ◽  
Author(s):  
Xiaodan Shao ◽  
Feng Chen
Keyword(s):  
Performance Analysis ◽  
General Complex ◽  
Noncircular Signals ◽  
Complex Valued

scholarly journals A Numerical Method for Computing the Roots of Non-Singular Complex-Valued Matrices

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 966
Author(s):  
Diego Caratelli ◽  
Paolo Emilio Ricci
Keyword(s):  
Numerical Method ◽  
Worked Examples ◽  
Higher Order ◽  
Singular Matrix ◽  
The Matrix ◽  
General Complex ◽  
Complex Valued

A method for the computation of the n th roots of a general complex-valued r × r non-singular matrix ? is presented. The proposed procedure is based on the Dunford–Taylor integral (also ascribed to Riesz–Fantappiè) and relies, only, on the knowledge of the invariants of the matrix, so circumventing the computation of the relevant eigenvalues. Several worked examples are illustrated to validate the developed algorithm in the case of higher order matrices.

scholarly journals General Complex-Valued Overlap Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ying Chen ◽  
Lvqing Bi ◽  
Bo Hu ◽  
Songsong Dai
Keyword(s):  
Fuzzy Sets ◽  
Aggregation Function ◽  
Construction Methods ◽  
General Complex ◽  
Complex Valued

Overlap function is a special type of aggregation function which measures the degree of overlapping between different classes. Recently, complex fuzzy sets have been successfully applied in many applications. In this paper, we extend the concept of overlap functions to the complex-valued setting. We introduce the notions of complex-valued overlap, complex-valued 0-overlap, complex-valued 1-overlap, and general complex-valued overlap functions, which can be regarded as the generalizations of the concepts of overlap, 0-overlap, 1-overlap, and general overlap functions, respectively. We study some properties of these complex-valued overlap functions and their construction methods.

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