A fast method to diagonalize a Hankel matrix
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Cited by
Sorted by citations
A comparison of nine PLS1 algorithms
Andersson, M. (2009) · Journal of Chemometrics · doi:10.1002/cem.1248 · Cited by 200 · see citing works
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics
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Löwner-Based Blind Signal Separation of Rational Functions With Applications
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“There is well-known theory about the factorization of Hankel matrices with the Vandermonde decomposition [8], [32], [33].”
MethodVandermonde factorization of Toeplitz matrices and applications in filtering and warping
Backstrom, T. (2013) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2013.2282271 · Cited by 26 · see citing works
“Observe that methods exist for fast factorization of with complexity [9].”
MethodKnockaert, L. F., Rogier, H., & Zutter, D. D. (2005) · AEU - International Journal of Electronics and Communications · doi:10.1016/j.aeue.2004.11.042 · Cited by 25 · see citing works
“In addition, modelling by exponential sums is inherent in linear systems theory [12] and its underlying Hankel matrix framework [13] [14].”
Fast and Robust Parametric Estimation of Jointly Sparse Channels
Barbotin, Y., & Vetterli, M. (2012) · IEEE Journal on Emerging and Selected Topics in Circuits and Systems · doi:10.1109/jetcas.2012.2214872 · Cited by 12 · see citing works
“Krylov approximants have received a lot of attention in the numerical analysis [24]–[27] or control theory [7], [28] literature, therefore we will only quickly skim through the subject.”
A Fast DVM Algorithm for Wideband Time-Delay Multi-Beam Beamformers
Perera, S. M., Lingsch, L., Madanayake, A., Mandal, S., & Mastronardi, N. (2022) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2022.3231182 · Cited by 11 · see citing works
“However, the factorization proposed in [38], [39], [40], [41] requires O(N2) operations to decompose Toeplitz and Hankel matrices via Vandermonde matrices.”
MethodThiran Filters for Wideband DSP-Based Multi-Beam True Time Delay RF Sensing Applications
Perera, S. M., Rathnasekara, G., & Madanayake, A. (2024) · Sensors · doi:10.3390/s24020576 · Cited by 5 · see citing works
Implementation And Evaluation Of The Vandermonde Transform
Bäckström, T., Boley, D. L., & Fischer, J. (2014) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.43749 · Cited by 5 · see citing works
Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
Chakrabarty, S., Mallick, B., Mukherjee, S., et al. (2026) · Physical Review A · doi:10.1103/lkcb-nqqb · Cited by 3 · see citing works
“The associated Hankel matrix H m ( q ), constructed from these moments, admits a Vandermonde decomposition of the form [79–81], where V m is the associated Vandermonde matrix: and Now, for an arbitrary vector x = ( x 1 , . . . , x m , x m + 1 ) ∈ R m + 1 , we have where, y = x V m = ( y 1 , y 2 , .…”
Sublinear-Time Algorithms for Compressive Phase Retrieval
Li, Y., & Nakos, V. (2020) · IEEE Transactions on Information Theory · doi:10.1109/tit.2020.3020701 · Cited by 2 · see citing works
“(1) 1 The runtime is dominated by Prony’s method, which can be implemented in O ( K 2 ) time using a Lanczos process (see, e.g. [35]) and solving a linear Vandermonde system (see, e.g. [36]).”
MethodOrthogonal Polynomials in Information Theory
Ahlswede, R. (2017) · Foundations in signal processing, communications and networking · doi:10.1007/978-3-319-53139-7_6 · Cited by 2 · see citing works
A new aspect of Hankel matrices via Krylov matrix
Cheon, G., & Kim, H. (2012) · Linear Algebra and its Applications · doi:10.1016/j.laa.2012.07.040 · Cited by 1 · see citing works
Sublinear-Time Algorithms for Compressive Phase RetrievalPreprint
Li, Y., & Nakos, V. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1709.02917
“(1) 1 The runtime is dominated by Prony’s method, which can be implemented in O ( K 2 ) time using a Lanczos process (see, e.g. [35]) and solving a linear Vandermonde system (see, e.g. [36]).”
MethodOn Hankel matrices and the symmetric nonnegative inverse eigenvalue problem
Julio, A. I., Dı́az, R. C., & Herrera, T. (2022) · Linear and Multilinear Algebra · doi:10.1080/03081087.2022.2159306
“For more details on Hankel matrices we refer the reader to [2–7].”
MethodA low-complexity structured neural network to realize states of dynamical systems
Aluvihare, H., Lingsch, L., Li, X., & Perera, S. M. (2026) · Linear Algebra and its Applications · doi:10.1016/j.laa.2026.08.036
Detection of quantum imaginarity using moments and its interferometric realization
Anonymous, Mukherjee, S., Maity, A. G., et al. (2026) · APS Open Science · doi:10.1103/828t-3czf
- Authors
- Boley, D. L., Luk, F. T., & Vandevoorde, D.
- Affiliations
- University of Minnesota (US)
- Rensselaer Polytechnic Institute (US)
- Corresponding author
- Boley, Daniel L.
- ORCID
- Boley, Daniel L.
- Venue
- Linear Algebra and its Applications
- Publisher
- Elsevier BV
- Published
- 1998-11
- Volume
- 284
- Issue
- 1-3
- Pages
- 41-52
- ISSN
- 0024-3795 (ISSN-L)
- OpenAlex
- W2029763612
- Cited by
- 17
- References
- 30
- Citations by year
- 2026: 3 · 2024: 1 · 2022: 2 · 2020: 1 · 2018: 1 · 2017: 1 · 2015: 1 · 2014: 1 · 2013: 1 · 2012: 2
- FWCI
- 0.47
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Linear Algebra and its Applications (publishedVersion)
- Funders
- National Science Foundation (9628786, 9405380)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Keywords
- Hankel matrices, diagonalization, Lanczos method, tridiagonal matrices, eigenvalue computation, modal decomposition
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