Rhaly terraced sequences their generalizations, properties and applications

Shannon, AG; Kuloğlu, B; Özkan, E

Rhaly terraced sequences their generalizations, properties and applications

Shannon, AG Kuloğlu, B Özkan, E

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Publisher:: SPRINGER HEIDELBERG
Publication Type:: Journal Article
Citation:: Computational and Applied Mathematics, 2025, 44, (5)
Issue Date:: 2025-07-01

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Field	Value	Language
dc.contributor.author	Shannon, AG
dc.contributor.author	Kuloğlu, B
dc.contributor.author	Özkan, E
dc.date.accessioned	2025-07-15T06:19:20Z
dc.date.available	2025-07-15T06:19:20Z
dc.date.issued	2025-07-01
dc.identifier.citation	Computational and Applied Mathematics, 2025, 44, (5)
dc.identifier.issn	2238-3603
dc.identifier.issn	1807-0302
dc.identifier.uri	http://hdl.handle.net/10453/188345
dc.description.abstract	This paper links terraced matrices with other well-known integer sequences, such as the Hankel matrices and related Fibonacci and Lucas matrices. These, in turn, are connected with related results of Macmahon and Sloane as well as we introduce the r-Terraced matrix as a generalization of the Terraced matrix, along with its symmetric counterpart, the symmetric r-Terraced matrix. We derive key properties of these matrices, including their spectral and Euclidean norms, upper bounds for their spreads, and characteristic polynomials. To validate and exemplify the theoretical findings, we apply them to Fibonacci numbers, providing illustrative examples that strengthen the theory and confirm its accuracy. In addition to the theoretical results, we investigated how the choice of the parameter r and the matrix dimension affect the upper bounds of the spread. Our findings reveal that selecting values of r<1 and using lower-dimensional matrices lead to tighter upper bounds while reducing computational complexity. These results highlight the practical benefits of our approach, particularly in optimization-related applications where efficiency is crucial.
dc.language	English
dc.publisher	SPRINGER HEIDELBERG
dc.relation.ispartof	Computational and Applied Mathematics
dc.relation.isbasedon	10.1007/s40314-025-03179-x
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	0102 Applied Mathematics, 0103 Numerical and Computational Mathematics
dc.subject.classification	Applied Mathematics
dc.subject.classification	4901 Applied mathematics
dc.subject.classification	4903 Numerical and computational mathematics
dc.title	Rhaly terraced sequences their generalizations, properties and applications
dc.type	Journal Article
utslib.citation.volume	44
utslib.for	0102 Applied Mathematics
utslib.for	0103 Numerical and Computational Mathematics
pubs.organisational-group	University of Technology Sydney
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	open_access	*
dc.rights.license	This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/
dc.date.updated	2025-07-15T06:19:19Z
pubs.issue	5
pubs.publication-status	Published
pubs.volume	44
utslib.citation.issue	5

Abstract:

This paper links terraced matrices with other well-known integer sequences, such as the Hankel matrices and related Fibonacci and Lucas matrices. These, in turn, are connected with related results of Macmahon and Sloane as well as we introduce the r-Terraced matrix as a generalization of the Terraced matrix, along with its symmetric counterpart, the symmetric r-Terraced matrix. We derive key properties of these matrices, including their spectral and Euclidean norms, upper bounds for their spreads, and characteristic polynomials. To validate and exemplify the theoretical findings, we apply them to Fibonacci numbers, providing illustrative examples that strengthen the theory and confirm its accuracy. In addition to the theoretical results, we investigated how the choice of the parameter r and the matrix dimension affect the upper bounds of the spread. Our findings reveal that selecting values of r<1 and using lower-dimensional matrices lead to tighter upper bounds while reducing computational complexity. These results highlight the practical benefits of our approach, particularly in optimization-related applications where efficiency is crucial.

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http://hdl.handle.net/10453/188345