Sequences of lower and upper bounds for the spectral radius of a nonnegative matrix.
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| Title: | Sequences of lower and upper bounds for the spectral radius of a nonnegative matrix. |
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| Authors: | Adam, Maria1 (AUTHOR) madam@dib.uth.gr, Oikonomou, Iro1 (AUTHOR), Aretaki, Aikaterini2 (AUTHOR) kathy@uth.gr |
| Source: | Linear Algebra & its Applications. Jun2023, Vol. 667, p165-191. 27p. |
| Subjects: | Nonnegative matrices, Mathematical bounds |
| Abstract: | In this article, we expand a classical Frobenius' result upon consecutive k -th powers of nonnegative matrices to establish sequences of new lower and upper bounds for the spectral radius with respect to the positive integer k , each term of which is formulated by the average (k + 1) -row sums of the nonnegative matrix. With the aid of the average (k + 1) -row sums and taking the extreme entries of the matrix, we study new bounds generalizing existing formulae and we produce sequences of new tighter approximations for the spectral radius. The monotonicity and convergence properties of the constructed sequences are explored and certain conditions are stated under which the new bounds are sharper than Frobenius' bounds and other existing formulae. We further characterize the cases of equality in the aforesaid bounds, when the matrix is irreducible. Throughout, we perform illustrative numerical examples to showcase the efficiency of our proposed bounds and make comparisons among them. [ABSTRACT FROM AUTHOR] |
| Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 162894062 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Sequences of lower and upper bounds for the spectral radius of a nonnegative matrix. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Adam%2C+Maria%22">Adam, Maria</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> madam@dib.uth.gr</i><br /><searchLink fieldCode="AR" term="%22Oikonomou%2C+Iro%22">Oikonomou, Iro</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Aretaki%2C+Aikaterini%22">Aretaki, Aikaterini</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> kathy@uth.gr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. Jun2023, Vol. 667, p165-191. 27p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Nonnegative+matrices%22">Nonnegative matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+bounds%22">Mathematical bounds</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this article, we expand a classical Frobenius' result upon consecutive k -th powers of nonnegative matrices to establish sequences of new lower and upper bounds for the spectral radius with respect to the positive integer k , each term of which is formulated by the average (k + 1) -row sums of the nonnegative matrix. With the aid of the average (k + 1) -row sums and taking the extreme entries of the matrix, we study new bounds generalizing existing formulae and we produce sequences of new tighter approximations for the spectral radius. The monotonicity and convergence properties of the constructed sequences are explored and certain conditions are stated under which the new bounds are sharper than Frobenius' bounds and other existing formulae. We further characterize the cases of equality in the aforesaid bounds, when the matrix is irreducible. Throughout, we perform illustrative numerical examples to showcase the efficiency of our proposed bounds and make comparisons among them. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=162894062 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.laa.2023.03.006 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 165 Subjects: – SubjectFull: Nonnegative matrices Type: general – SubjectFull: Mathematical bounds Type: general Titles: – TitleFull: Sequences of lower and upper bounds for the spectral radius of a nonnegative matrix. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Adam, Maria – PersonEntity: Name: NameFull: Oikonomou, Iro – PersonEntity: Name: NameFull: Aretaki, Aikaterini IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 06 Text: Jun2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 00243795 Numbering: – Type: volume Value: 667 Titles: – TitleFull: Linear Algebra & its Applications Type: main |
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