The smallest eigenvalue of the Hankel matrices associated with a perturbed Jacobi weight
Authors: 
Yuxi Wang, Yang ChenAuthors Info & Claims
References
[1]
E. Telatar, Capacity of multi-antenna Gaussian channels, Eur. Trans. Telecommun. 10 (6) (1999) 585–595,.
[2]
G.J. Foschini, M.J. Gans, On the limit of wireless communications in fading environment when using multiple antennas, Wirel. Pers. Commun. 6 (1998) 311–335,.
[3]
M. Chiani, M.Z. Win, A. Zanella, On the capacity of spatially correlated MIMO Rayleigh-fading channels, IEEE Trans. Inf. Theory 49 (10) (2003) 2363–2371,.
[4]
M.R. Mckay, I.B. Collings, General capacity bounds for spatially correlated Rician MIMO channels, IEEE Trans. Inf. Theory 51 (9) (2005) 3121–3145,.
[5]
Y. Chen, M.R. McKay, Coulumb fluid, Painlevé transcendents, and the information theory of MIMO systems, IEEE Trans. Inf. Theory 58 (7) (2012) 4594–4634,.
[6]
H. Chen, M. Chen, G. Blower, et al., Single-user MIMO system, Painlevé transcendents, and double scaling, J. Math. Phys. 58 (12) (2017),.
[7]
Chen, Y.; McKay, M.R. (2010): Perturbed Hankel determinants: applications to the information theory of MIMO wireless communications. arXiv preprint https://doi.org/10.48550/arXiv.1007.0496.
[8]
N.J. Higham, F. Tisseur, More on pseudospectra for polynomial eigenvalue problems and applications in control theory, Linear Algebra Appl. 351 (2002) 435–453,.
[9]
N. Emmart, Y. Chen, C.C. Weems, Computing the smallest eigenvalue of large ill-conditioned Hankel matrices, Commun. Comput. Phys. 18 (1) (2015) 104–124,.
[10]
Y. Chen, D.S. Lubinsky, Smallest eigenvalues of Hankel matrices for exponential weights, J. Math. Anal. Appl. 293 (2) (2004) 476–495,.
[11]
F. De Mari, H.G. Feichtinger, K. Nowak, Uniform eigenvalue estimates for time-frequency localization operators, J. Lond. Math. Soc. 65 (3) (2002) 720–732,.
[12]
J. Khodaparast, O.B. Fosso, M. Molinas, J.A. Suul, Static and dynamic eigenvalues in unified stability studies, IET Gener. Transm. Distrib. 16 (17) (2022) 3563–3577,.
[13]
M.E.H. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, 2005,.
[14]
H. Widom, H. Wilf, Small eigenvalues of large Hankel matrices, Proc. Am. Math. Soc. 17 (2) (1966) 338–344,.
[15]
G. Szegö, Orthogonal Polynomials, American Mathematical Society, Rhode Island, 1939.
[16]
G. Szegö, On some Hermitian forms associated with two given curves of the complex plane, Trans. Am. Math. Soc. 40 (1936) 450–461,.
[17]
G. Pólya, G. Szegö, Problems and Theorems in Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 1976,.
[18]
H.S. Wilf, Finite Sections of Some Classical Inequalities, Springer, Berlin, Heidelberg, 1970,.
[19]
Y. Chen, N. Lawrence, Small eigenvalues of large Hankel matrices, J. Phys. A, Math. Gen. 32 (42) (1999) 7305–7315,.
[20]
M. Zhu, Y. Chen, N. Emmart, C. Weems, The smallest eigenvalue of large Hankel matrices, Appl. Math. Comput. 334 (2018) 375–387,.
[21]
Y. Chen, J. Sikorowski, M. Zhu, Smallest eigenvalue of large Hankel matrices at critical point: comparing conjecture with parallelised computation, Appl. Math. Comput. 363 (2019),.
[22]
M. Zhu, N. Emmart, Y. Chen, C. Weems, The smallest eigenvalue of large Hankel matrices generated by a deformed Laguerre weight, Math. Methods Appl. Sci. 42 (2019) 3272–3288,.
[23]
G. Szegö, Hankel Forms, (English translation of A Hankel-féle formákról), Collected papers, 1 Birkhäuser, Basle, 1982, p. P111.
[24]
M. Zhu, Y. Chen, C. Li, The smallest eigenvalue of large Hankel matrices generated by a singularly perturbed Laguerre weight, J. Math. Phys. 61 (7) (2020),.
[25]
L. Zhan, G. Blower, Y. Chen, M. Zhu, Center of mass distribution of the Jacobi unitary ensembles: Painlevé V, asymptotic expansions, J. Math. Phys. 59 (10) (2018),.
[26]
D. Wang, M. Zhu, Y. Chen, The smallest eigenvalue of large Hankel matrices associated with a singularly perturbed Gaussian weight, Proc. Am. Math. Soc. 150 (1) (2020) 153–160,.
Recommendations
The smallest eigenvalue of large Hankel matrices
AbstractWe investigate the large N behavior of the smallest eigenvalue, λN , of an ( N + 1 ) × ( N + 1 ) Hankel (or moments) matrix H N , generated by the weight w ( x ) = x α ( 1 − x ) β , x ∈ [ 0 , 1 ] , α > − 1 , β > − 1. By ...
Smallest eigenvalue of large Hankel matrices at critical point: Comparing conjecture with parallelised computation
AbstractWe propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill-conditioned Hankel matrices. It is based on the LDLT decomposition and involves finding a k × k sub-matrix of the inverse of the ...
Asymptotics of determinants of Hankel matrices via non-linear difference equations
E. Heine in the 19th century studied a system of orthogonal polynomials associated with the weight x ( x - α ) ( x - ) - 1 2 , x 0 , α , 0 < α < . A related system was studied by C. J. Rees in 1945, associated with the weight ( 1 - x 2 ) ( 1 - k 2 x 2 ) ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
Elsevier Inc.
Publisher
Elsevier Science Inc.
United States
Publication History
Published: 17 July 2024
Author Tags
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 26 Dec 2024