Back to Search
Start Over
Estimate of the Spectrum of Discrete Sequences in Ill-Posed Problems Based on the Study of the Numerical Rank of the Trajectory Matrix.
- Source :
-
Journal of Mathematical Sciences . Mar2024, Vol. 279 Issue 5, p644-654. 11p. - Publication Year :
- 2024
-
Abstract
- In this paper, we discuss properties of the singular value decomposition (SVD-decomposition) within the framework of the analysis of the numerical rank in ill-posed problems for determining frequency properties of discrete sequences consisting of trigonometric binomials. The properties of the numerical rank of the SVD-decomposition are indicated. We propose an algorithm for determining the frequencies of trigonometric binomials involved in the original function that forms a discrete sequence; this algorithm is based on estimates of the numerical rank. We obtain a stable criterion for estimating the numerical rank based on the arithmetic-mean estimators of the pseudo-null-space of the trajectory matrix. Also, we present the results of numerical experiments that demonstrate the consistency of the arithmetic-mean estimator of the pseudo-zero-space for the analysis of the spectrum of noisy sequences. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10723374
- Volume :
- 279
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 176452265
- Full Text :
- https://doi.org/10.1007/s10958-024-07045-9