Оптимизация сингулярных чисел матриц, зависящих от параметров…
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2016. № 5
65
[8] Derevtsov E.Y., Efimov A.V., Louis A.K., Schuster T. Singular value decomposition and
its application to numerical inversion for ray transforms in 2D vector tomography.
Journal
of Inverse and Ill-posed Problems
, 2011, vol. 19, no. 4–5, pp. 689–715.
[9] Mironovskiy L.A., Solov'eva T.N. Analysis of multiplicity of Hankel singular values
of control systems.
Automation and Remote Control
, 2015, vol. 76, iss. 2, pp. 205–218.
DOI: 10.1134/S0005117915020022
[10] Miszczak J.A. Singular value decomposition and matrix reorderings in quantum infor-
mation theory.
International Journal of Modern Physics C
. 2011.
DOI: 10.1142/S0129183111016663
[11] Lee N., Cichocki A
.
Estimating a few extreme singular values and vectors for large-scale
matrices in tensor train format.
SIAM Journal on Matrix Analysis and Applications
, 2015,
vol. 36, no. 3, pp. 994–1014.
[12] Montaño E., Salas M., Sóto R.L
.
Nonnegative matrices with prescribed extremal singular
values.
Computers and Mathematics with Applications
, 2008, vol. 56, no. 1, pp. 30–42.
[13] Lewis A.S., Sendov H.S. Nonsmooth analysis of singular values.
Set-Valued and Varia-
tional Analysis
, 2005, vol. 13, no. 3, pp. 213–241.
[14] Chen X., Li W. Sensitivity analysis for the generalized singular value decomposition.
Nu-
merical Linear Algebra with Applications
, 2013, vol. 20, no. 1, pp. 138–149.
[15] Zhang L., Zhang N., Xiao X
.
On the second-order directional derivatives of singular
values of matrices and symmetric matrix-valued functions.
Set-Valued and Variational
Analysis
, 2013, vol. 21, no. 3, pp. 557–586.
[16] Chu M.T., Lin M.M., Wang L
.
A study of singular spectrum analysis with global optimiza-
tion techniques.
Journal of Global Optimization
, 2014, vol. 60, no. 2, pp. 551–574.
[17] Liang Q., Ye Q
.
Computing singular values of large matrices with an inverse-free precon-
ditioned Krylov subspace method.
Electronic Transactions on Numerical Analysis
, 2014,
vol. 42, pp. 197–221.
[18] Wu L., Stathopoulos A
.
A preconditioned hybrid SVD method for computing accurately
singular triplets of large matrices.
SIAM Journal on Scientific Computing
, 2015, vol. 37, no. 5,
pp. S365–S388.
[19] Floudas C.A., Gounaris C.E. A review of recent advances in global optimization.
Journal
of Global Optimization
, 2009, vol. 45, no. 1, pp. 3–38.
[20] Lera D., Sergeev Ya.D. Deterministic global optimization using space-filling curves and
multiple estimates of Lipschitz and Hölder constants.
Computations in Nonlinear Science and
Numerical Simulations
, 2015, vol. 23, no. 1–3, pp. 326–342.
[21] Luz E.F.P., Becceneri J.C., De Campos Velho H.F
.
A new multi-particle collision algo-
rithm for optimization in a high performance environment.
Journal of Computational Inter-
disciplinary Sciences
, 2008, vol. 1, pp. 3–10.
[22] Rios-Coelho A.C., Sacco W.f., Henderson N. A Metropolis algorithm combined with
Hooke-Jeeves local search method applied to global optimization.
Applied Mathematics and
Computation
, 2010, vol. 217, no. 2, pp. 843–845.
[23] Voglis C., Parsopoulos K.E., Papageorgiou D.G., Lagaris I.E., Vrahatis M.N
.
MEMP-
SODE: A global optimization software based on hybridization of population-based algorithms
and local searches.
Computer Physics Communications
, 2012, vol. 183, no. 2, pp. 1139–1154.