An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications

In this paper, we extend notions of complex C−R$\mathbb {C} - \mathbb {R}$‐calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical re...

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Vydáno v:Mathematische Nachrichten Ročník 297; číslo 2; s. 454 - 481
Hlavní autoři: Alpay, Daniel, Diki, Kamal, Vajiac, Mihaela
Médium: Journal Article
Jazyk:angličtina
Vydáno: Weinheim Wiley Subscription Services, Inc 01.02.2024
Témata:
Algorithms
BC−R$\mathbb {BC}-\mathbb {R}$ calculus
bicomplex gradient operator
bicomplex numbers
BLMS algorithm
C–R calculus
ISSN:0025-584X, 1522-2616
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Shrnutí:In this paper, we extend notions of complex C−R$\mathbb {C} - \mathbb {R}$‐calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202200475