Previous Page  20 / 21 Next Page
Information
Show Menu
Previous Page 20 / 21 Next Page
Page Background

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.