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...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische Nachrichten Vol. 297; no. 2; pp. 454 - 481
Main Authors: Alpay, Daniel, Diki, Kamal, Vajiac, Mihaela
Format: Journal Article
Language:English
Published: Weinheim Wiley Subscription Services, Inc 01.02.2024
Subjects:
Algorithms
BC−R$\mathbb {BC}-\mathbb {R}$ calculus
bicomplex gradient operator
bicomplex numbers
BLMS algorithm
C–R calculus
ISSN:0025-584X, 1522-2616
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202200475