Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
