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Approximate singular values of the fractional difference and summation operators

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Title: Approximate singular values of the fractional difference and summation operators
Authors: Burman, Prabir1 burman@wald.ucdavis.edu
Source: Linear Algebra & its Applications. Jul2006, Vol. 416 Issue 2/3, p677-687. 11p.
Subjects: Matrices (Mathematics), Eigenvalues, Linear operators, Universal algebra
Abstract: Abstract: We obtain sharp bounds on the singular values of the fractional difference and summation operators on R n . These bounds allow us to establish that the convergence rates of the distributions of the singular values of these operators are O(1/n). Since the fractional difference operator of order α is associated with the Toeplitz matrix with Fisher–Hartwig symbol (2−2cos u) α , α >0, we are able to obtain similar bounds on the eigenvalues of this Toeplitz matrix and a similar result on the convergence rate of the distribution of its eigenvalues. [Copyright &y& Elsevier]
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
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DbLabel: Engineering Source
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  Data: Approximate singular values of the fractional difference and summation operators
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  Data: Abstract: We obtain sharp bounds on the singular values of the fractional difference and summation operators on R n . These bounds allow us to establish that the convergence rates of the distributions of the singular values of these operators are O(1/n). Since the fractional difference operator of order α is associated with the Toeplitz matrix with Fisher–Hartwig symbol (2−2cos u) α , α >0, we are able to obtain similar bounds on the eigenvalues of this Toeplitz matrix and a similar result on the convergence rate of the distribution of its eigenvalues. [Copyright &y& Elsevier]
– 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.)
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        Value: 10.1016/j.laa.2005.12.014
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      – Code: eng
        Text: English
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      – SubjectFull: Eigenvalues
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      – TitleFull: Approximate singular values of the fractional difference and summation operators
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              Text: Jul2006
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