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Journal articles on the topic 'Perturbation matrix'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

AROUNA, Traoré G. Y., Famane KAMBIRE, and Sylvestre P. EKRA. "PERTURBATION ANALYSIS OF SYMPLECTIC MATRIX." International Journal of Numerical Methods and Applications 38, no. 1 (2025): 187–209. https://doi.org/10.17654/0975045225008.

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Starting a theory of perturbation introduced by Arouna et al. [1], perturbations preserving the -symplecticity structure of a symplectic matrix are presented. Results on the consequences of the effect of a rank- perturbation on the strong stability of this type of matrix are proposed. Two numerical examples are given to analyze the effect of these perturbations on the strong stability and spectrum of symplectic matrices.

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2

Zhang, Jiafan, Jianping Ye, Huajiang Ouyang, and Xiang Yin. "An explicit formula of perturbating stiffness matrix for partial natural frequency assignment using static output feedback." Journal of Low Frequency Noise, Vibration and Active Control 37, no. 4 (2018): 1045–52. http://dx.doi.org/10.1177/1461348418756026.

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The partial eigenvalue (or natural frequency) assignment or placement, only by the stiffness matrix perturbation, of an undamped vibrating system is addressed in this paper. A novel and explicit formula of determining the perturbating stiffness matrix is deduced from the eigenvalues perturbation theorem for a low-rank perturbed matrix. This formula is then utilized to solve the partial eigenvalue (or natural frequency) assignment via the static output feedback. The control matrix, output matrix and feedback gain matrix can be explicitly expressed and easily constructed.

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3

Wu, Zhenqing, Zhejun Huang, Sijin Wu, Ziying Yu, Liuxin Zhu, and Lili Yang. "Accelerating Convergence of Langevin Dynamics via Adaptive Irreversible Perturbations." Mathematics 12, no. 1 (2023): 118. http://dx.doi.org/10.3390/math12010118.

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Irreversible perturbations in Langevin dynamics have been widely recognized for their role in accelerating convergence in simulations of multi-modal distributions π(θ). A commonly used and easily computed standard irreversible perturbation is J∇logπ(θ), where J is a skew-symmetric matrix. However, Langevin dynamics employing a fixed-scale standard irreversible perturbation encounter a trade-off between local exploitation and global exploration, associated with small and large scales of standard irreversible perturbation, respectively. To address this trade-off, we introduce the adaptive irreve

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4

Angelova, Vera, and Petko Petkov. "Componentwise Perturbation Analysis of the Singular Value Decomposition of a Matrix." Applied Sciences 14, no. 4 (2024): 1417. http://dx.doi.org/10.3390/app14041417.

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A rigorous perturbation analysis is presented for the singular value decomposition (SVD) of a real matrix with full column rank. It is proved that the SVD perturbation problem is well posed only when the singular values are distinct. The analysis involves the solution of symmetric coupled systems of linear equations. It produces asymptotic (local) componentwise perturbation bounds on the entries of the orthogonal matrices participating in the decomposition of the given matrix and on its singular values. Local bounds are derived for the sensitivity of the singular subspaces measured by the angl

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5

Texier, Benjamin. "Basic matrix perturbation theory." L’Enseignement Mathématique 64, no. 3 (2019): 249–63. http://dx.doi.org/10.4171/lem/64-3/4-1.

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6

Kay, Jun Kyung, and Hyun Mee Kim. "Characteristics of Initial Perturbations in the Ensemble Prediction System of the Korea Meteorological Administration." Weather and Forecasting 29, no. 3 (2014): 563–81. http://dx.doi.org/10.1175/waf-d-13-00097.1.

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Abstract In this study, the initial ensemble perturbation characteristics of the new Korea Meteorological Administration (KMA) ensemble prediction system (EPS), a version of the Met Office Global and Regional Ensemble Prediction System, were analyzed over two periods: from 1 June to 31 August 2011, and from 1 December 2011 to 29 February 2012. The KMA EPS generated the initial perturbations using the ensemble transform Kalman filter (ETKF). The observation effect was reflected in both the transform matrix and the inflation factor of the ETKF; it reduced (increased) uncertainties in the initial

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7

Yonchev, A. "Perturbation Analysis of the Continuous-time Regional Pole Assignment and H2 Performance Control Problems: an LMI Approach." Information Technologies and Control 12, no. 3-4 (2014): 28–35. http://dx.doi.org/10.1515/itc-2016-0004.

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Abstract In the paper a method to conduct perturbation analysis of regional pole assignment and H2 performance control problems for linear continuous-time systems are investigated. The studied control problems are based on solving LMIs (Linear Matrix Inequalities) and applying Lyapunov functions. The problem of performing sensitivity analysis of the perturbed matrix inequalities is done in a similar way as for perturbed matrix equations, after introducing a slightly perturbed right hand part. The calculated perturbation bounds can be used to analyze the feasibility and performance of the consi

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8

Isabel García-Planas, M., and Tetiana Klymchuk. "Perturbation analysis of a matrix differential equation ẋ = ABx." Applied Mathematics and Nonlinear Sciences 3, no. 1 (2018): 97–104. http://dx.doi.org/10.21042/amns.2018.1.00007.

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AbstractTwo complex matrix pairs (A, B) and (A′, B′) are contragrediently equivalent if there are nonsingular S and R such that (A′, B′) = (S−1AR, R−1BS). M.I. García-Planas and V.V. Sergeichuk (1999) constructed a miniversal deformation of a canonical pair (A, B) for contragredient equivalence; that is, a simple normal form to which all matrix pairs (A + A͠, B + B͠) close to (A, B) can be reduced by contragredient equivalence transformations that smoothly depend on the entries of A͠ and B͠. Each perturbation (A͠, B͠) of (A, B) defines the first order induced perturbation AB͠ + A͠B of the matr

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9

Bahloul, Aymen. "Spectral properties for unbounded block operator matrices via polynomially Riesz perturbations." Filomat 38, no. 16 (2024): 5655–67. https://doi.org/10.2298/fil2416655b.

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As well-known, the perturbation theory of polynomially Riesz operators is an attractive way to characterize certain spectral analysis in Fredholm theory, it is also a tool of great significance in the matrix framework. The first aim of this paper is to find some new arguments of perturbations allowing us to provide some original left-right Fredholm properties of 3 ? 3 unbounded block operator matrix form defined with maximal domain and to provide an amelioration and a continuation of the recent work invested by Abdmouleh, Khlif and Walha in [Spectral description of Fredholm operators via polyn

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10

Putinar, Mihai, and Dmitry Yakubovich. "Spectral dissection of finite rank perturbations of normal operators." Journal of Operator Theory 85, no. 1 (2020): 45–78. http://dx.doi.org/10.7900/jot.2019jul21.2266.

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Finite rank perturbations T=N+K of a bounded normal operator N acting on a separable Hilbert space are studied thanks to a natural functional model of T; in its turn the functional model solely relies on a perturbation matrix/characteristic function previously defined by the second author. Function theoretic features of this perturbation matrix encode in a closed-form the spectral behavior of T. Under mild geometric conditions on the spectral measure of N and some smoothness constraints on K we show that the operator T admits invariant subspaces, or even it is decomposable.

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11

Topor, Nadia. "Perturbation Method for Boundary S-Matrix in 2D Quantum Field Theory." Modern Physics Letters A 12, no. 38 (1997): 2951–62. http://dx.doi.org/10.1142/s0217732397003071.

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We develop a perturbation theory for evaluating the boundary S-matrix in 2D quantum field theory. We apply this approach to calculate the one-loop boundary S-matrix for the elementary particle of the sine–Gordon model with a boundary interaction. Our perturbative result agrees with the exact expression of the S-matrix conjectured by Goshal; it also allows us to derive the perturbative relation between the parameter ϑ in the S-matrix and the free parameter M in the boundary action, in the particular case in which its other free parameter φ0 is zero.

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12

Batzke, Leonhard. "Sign Characteristics of Regular Hermitian Matrix Pencils under Generic Rank-1 and Rank-2 Perturbations." Electronic Journal of Linear Algebra 30 (February 8, 2015): 760–94. http://dx.doi.org/10.13001/1081-3810.2014.

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The spectral behavior of regular Hermitian matrix pencils is examined under certain structure-preserving rank-1 and rank-2 perturbations. Since Hermitian pencils have signs attached to real (and infinite) blocks in canonical form, it is not only the Jordan structure but also this so-called sign characteristic that needs to be examined under perturbation. The observed effects are as follows: Under a rank-1 or rank-2 perturbation, generically the largest one or two, respectively, Jordan blocks at each eigenvalue lambda are destroyed, and if lambda is an eigenvalue of the perturbation, also one n

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13

Angelova, Vera, Mustapha Hached, and Khalide Jbilou. "Sensitivity of the Solution to Nonsymmetric Differential Matrix Riccati Equation." Mathematics 9, no. 8 (2021): 855. http://dx.doi.org/10.3390/math9080855.

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Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition. Two approaches of nonlocal perturbation analysis of the symmetric differential Riccati equation are extended to the nonsymmetric case. Applying the techniques of Fréchet derivatives, Lyapunov majorants and fixed-point principle, two perturbation bounds are derived: the first one is based on the integral form of the solution and the second one considers the equ

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14

Huang, Jiaoyang. "Mesoscopic perturbations of large random matrices." Random Matrices: Theory and Applications 07, no. 02 (2018): 1850004. http://dx.doi.org/10.1142/s2010326318500041.

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We consider the eigenvalues and eigenvectors of small rank perturbations of random [Formula: see text] matrices. We allow the rank of perturbation [Formula: see text] to increase with [Formula: see text], and the only assumption is [Formula: see text]. The spiked population model, proposed by Johnstone [On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist. 29(2) (2001) 295–327], is of this kind, in which all the population eigenvalues are 1’s except for a few fixed eigenvalues. Our model is more general since we allow the number of non-unit population ei

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15

Petkov, Petko H. "Componentwise Perturbation Analysis of the QR Decomposition of a Matrix." Mathematics 10, no. 24 (2022): 4687. http://dx.doi.org/10.3390/math10244687.

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The paper presents a rigorous perturbation analysis of the QR decomposition A=QR of an n×m matrix A using the method of splitting operators. New asymptotic componentwise perturbation bounds are derived for the elements of Q and R and the subspaces spanned by the first p≤m columns of A. The new bounds are less conservative than the known bounds and are significantly better than the normwise bounds. An iterative scheme is proposed to determine global componentwise bounds in the case of perturbations for which such bounds are valid. Several numerical results are given that illustrate the analysis

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16

Yonchev, A. "Perturbation Analysis of the LMI-Based Continuous-time Linear Quadratic Regulator Problem for Descriptor Systems." Information Technologies and Control 14, no. 1 (2016): 13–20. http://dx.doi.org/10.1515/itc-2016-0017.

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Abstract This paper considers an approach to perform perturbation analysis of linear quadratic regulator (LQR) control problem for continuous-time descriptor systems. The investigated control problem is based on solving LMIs (Linear Matrix Inequalities) and applying Lyapunov functions. The paper is concerned with obtaining linear perturbation bounds for the continuous-time LQR control problem for descriptor systems. The computed perturbation bounds can be used to study the effect of perturbations in system and controller on feasibility and performance of the considered control problem. A numer

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17

Ahmadnasab, Morad, and Panayiotis J. Psarrakos. "Eigenvalue characterization of some structured matrix pencils under linear perturbation." Electronic Journal of Linear Algebra 40 (February 20, 2024): 274–98. http://dx.doi.org/10.13001/ela.2024.7371.

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We study the effect of linear perturbations on three families of matrix pencils. The matrix pairs of the first two families are Hermitian/skew-Hermitian with special $3\times 3$ block cases appeared in continuous-time control, and the matrix pairs of the third family are special $3\times 3$ non-Hermitian block matrices appeared in discrete-time control. For the first family of matrix pencils and more general cases of the second family of matrix pencils, based on the properties of the involved matrices, we obtain some upper or lower bounds on the set of eigenvalues of linearly perturbed matrix

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18

Neumann, Niels, and Walter van Suijlekom. "Perturbation semigroup of matrix algebras." Journal of Noncommutative Geometry 10, no. 1 (2016): 241–60. http://dx.doi.org/10.4171/jncg/233.

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19

Niklasson, Anders M. N., Valéry Weber, and Matt Challacombe. "Nonorthogonal density-matrix perturbation theory." Journal of Chemical Physics 123, no. 4 (2005): 044107. http://dx.doi.org/10.1063/1.1944725.

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20

Choque-Rivero, Abdon E., and Luis E. Garza. "Moment perturbation of matrix polynomials." Integral Transforms and Special Functions 26, no. 3 (2014): 177–91. http://dx.doi.org/10.1080/10652469.2014.978866.

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21

Bhatia, Rajendra. "Review of matrix perturbation theory." Linear Algebra and its Applications 160 (January 1992): 255–59. http://dx.doi.org/10.1016/0024-3795(92)90451-f.

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22

Masoudi, Mohsen, and Abbas Salemi. "Perturbation bounds for matrix functions." Mathematical Inequalities & Applications, no. 3 (2020): 1105–15. http://dx.doi.org/10.7153/mia-2020-23-84.

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23

Liu, J. K., and H. C. Chan. "Universal Matrix Perturbation Method for Structural Dynamic Reanalysis of General Damped Gyroscopic Systems." Journal of Vibration and Control 10, no. 4 (2004): 525–41. http://dx.doi.org/10.1177/1077546304036230.

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We investigate an effective matrix perturbation method for structural dynamic reanalysis of general damped gyroscopic systems. By using the complex eigensubspace condensation and the or thogonal decomposition procedures, two greatly reduced generalized eigenvalue equations are obtained. The lower-order perturbations of eigensolutions (i.e. complex eigenvalues and the corresponding left and right eigenvectors) are then determined by solving the two reduced eigenvalue problems. The higher-order perturbations of eigensolutions are obtained by executing a singular value decomposition procedure for

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24

Jerry T. Barretto, Jerry T. Barretto, Clark Kendrick C. Go Clark Kendrick C. Go, and Stein Alec C. Baluyot Stein Alec C. Baluyot. "Ray transfer matrix perturbation for an optical component with aberration." Chinese Optics Letters 10, no. 8 (2012): 080801–80803. http://dx.doi.org/10.3788/col201210.080801.

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25

Lenard, Christopher T. "Rank-1 perturbations and the Lanczos method, inverse iteration, and Krylov subspaces." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 36, no. 4 (1995): 381–88. http://dx.doi.org/10.1017/s0334270000007438.

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AbstractThe heart of the Lanczos algorithm is the systematic generation of orthonormal bases of invariant subspaces of a perturbed matrix. The perturbations involved are special since they are always rank-1 and are the smallest possible in certain senses. These minimal perturbation properties are extended here to more general cases.Rank-1 perturbations are also shown to be closely connected to inverse iteration, and thus provide a novel explanation of the global convergence phenomenon of Rayleigh quotient iteration.Finally, we show that the restriction to a Krylov subspace of a matrix differs

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26

Dohmen, Janik, and Harro Schmeling. "Magma ascent mechanisms in the transition regime from solitary porosity waves to diapirism." Solid Earth 12, no. 7 (2021): 1549–61. http://dx.doi.org/10.5194/se-12-1549-2021.

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Abstract. In partially molten regions inside the Earth, melt buoyancy may trigger upwelling of both solid and fluid phases, i.e., diapirism. If the melt is allowed to move separately with respect to the matrix, melt perturbations may evolve into solitary porosity waves. While diapirs may form on a wide range of scales, porosity waves are restricted to sizes of a few times the compaction length. Thus, the size of a partially molten perturbation in terms of compaction length controls whether material is dominantly transported by porosity waves or by diapirism. We study the transition from diapir

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27

Surján, Peter R., and Ágnes Szabados. "Convergence Enhancement in Perturbation Theory." Collection of Czechoslovak Chemical Communications 69, no. 1 (2004): 105–20. http://dx.doi.org/10.1135/cccc20040105.

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The Frobenius norm of operator QW is minimized with respect to level shift parameters applied to the zero-order spectrum, where W is the perturbation while Q is the reduced resolvent of the zero-order Hamiltonian. The stationary condition leads to a simple formula for the level shifts which eliminates degeneracy-induced singularities. Such level shifts may increase the radius of convergence of the perturbation series, and may improve low-order perturbative estimations - as it is found in the cases of a simple matrix eigenvalue problem and the one-dimensional quartic anharmonic oscillator.

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28

Gaeta, G., and G. Pucacco. "Near-resonances and detuning in classical and quantum mechanics." Mathematics in Engineering 5, no. 1 (2022): 1–44. http://dx.doi.org/10.3934/mine.2023005.

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<abstract><p>From the point of view of perturbation theory, (perturbations of) near-resonant systems are plagued by small denominators. These do not affect (perturbations of) fully resonant systems; so it is in many ways convenient to approximate near resonant systems as fully resonant ones, which correspond to considering the "detuning" as a perturbation itself. This approach has proven very fruitful in Classical Mechanics, but it is also standard in (perturbations of) Quantum Mechanical systems. Actually, its origin may be traced back (at least) to the Rayleigh-Ritz method for co

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29

MONAHAN, C. J. "THE BEAUTY OF LATTICE PERTURBATION THEORY: THE ROLE OF LATTICE PERTURBATION THEORY IN B PHYSICS." Modern Physics Letters A 27, no. 37 (2012): 1230040. http://dx.doi.org/10.1142/s0217732312300406.

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As new experimental data arrive from the LHC the prospect of indirectly detecting new physics through precision tests of the Standard Model grows more exciting. Precise experimental and theoretical inputs are required to test the unitarity of the CKM matrix and to search for new physics effects in rare decays. Lattice QCD calculations of non-perturbative inputs have reached a precision at the level of a few percent; in many cases aided by the use of lattice perturbation theory. This review examines the role of lattice perturbation theory in B physics calculations on the lattice in the context

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30

Baruh, H. "Pole Allocation Using Matrix Perturbations." Journal of Dynamic Systems, Measurement, and Control 109, no. 2 (1987): 189–91. http://dx.doi.org/10.1115/1.3143839.

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An approach is presented for pole placement in controllers and observers. The first-order perturbation of the system eigensolution is used to analyze and design the feedback gains. The accuracy of the control (or observer) design depends on how small a perturbation the control gains are on the uncontrolled system, and it is assessed qualitatively and quantitatively.

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31

ANIELLO, PAOLO. "PERTURBATIVE SOLUTIONS OF DIFFERENTIAL EQUATIONS IN LIE GROUPS." International Journal of Geometric Methods in Modern Physics 02, no. 01 (2005): 111–25. http://dx.doi.org/10.1142/s0219887805000478.

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We show that, given a matrix Lie group [Formula: see text] and its Lie algebra [Formula: see text], a 1-parameter subgroup of [Formula: see text] whose generator is the sum of an unperturbed matrix Â0 and an analytic perturbation Â♢(λ) can be mapped — under suitable conditions — by a similarity transformation depending analytically on the perturbative parameter λ, onto a 1-parameter subgroup of [Formula: see text] generated by a matrix [Formula: see text] belonging to the centralizer of Â0 in [Formula: see text]. Both the similarity transformation and the matrix [Formula: see text] can be dete

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32

Chacha, Chacha Stephen, and Syed Muhammad Raza Shah Naqvi. "Condition Numbers of the Nonlinear Matrix Equation Xp-A⁎eXA=I." Journal of Function Spaces 2018 (August 1, 2018): 1–8. http://dx.doi.org/10.1155/2018/3291867.

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We explore the condition numbers of the nonlinear matrix equation Xp-A⁎eXA=I. Explicit expressions for the normwise, mixed, and componentwise condition numbers are derived. The upper bounds for the mixed and componentwise condition numbers are obtained. The numerical result favors the fact that our estimations are fairly sharp. Also, the relative upper perturbation bounds give satisfactory results for small perturbations in the input data.

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33

Mayfield, M. Elizabeth. "Perturbation of a Tridiagonal Stability Matrix." Mathematics Magazine 67, no. 2 (1994): 124. http://dx.doi.org/10.2307/2690686.

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34

Avrachenkov, K. E., and J. B. Lasserre. "Analytic perturbation of Sylvester matrix equations." IEEE Transactions on Automatic Control 47, no. 7 (2002): 1116–19. http://dx.doi.org/10.1109/tac.2002.800649.

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35

Truflandier, Lionel A., Rivo M. Dianzinga, and David R. Bowler. "Notes on density matrix perturbation theory." Journal of Chemical Physics 153, no. 16 (2020): 164105. http://dx.doi.org/10.1063/5.0022244.

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36

Gohberg, I., P. Lancaster, and L. Rodman. "Perturbation of analytic hermitian matrix functions." Applicable Analysis 20, no. 1-2 (1985): 23–48. http://dx.doi.org/10.1080/00036818508839556.

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37

Konstantinov, M. M., P. Hr Petkov, and N. D. Christov. "Perturbation Analysis of Matrix Quadratic Equations." SIAM Journal on Scientific and Statistical Computing 11, no. 6 (1990): 1159–63. http://dx.doi.org/10.1137/0911065.

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38

Mayfield, M. Elizabeth. "Perturbation of a Tridiagonal Stability Matrix." Mathematics Magazine 67, no. 2 (1994): 124–27. http://dx.doi.org/10.1080/0025570x.1994.11996198.

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39

Killingbeck, J. P., and G. Jolicard. "Perturbation methods for the matrix eigenproblem." Journal of Physics A: Mathematical and General 25, no. 23 (1992): 6455–59. http://dx.doi.org/10.1088/0305-4470/25/23/037.

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40

Tang, Fu Cheng. "Perturbation techniques for fuzzy matrix equations." Fuzzy Sets and Systems 109, no. 3 (2000): 363–69. http://dx.doi.org/10.1016/s0165-0114(98)00021-9.

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41

Baragaña, I., V. Fernández, and I. Zaballa. "Perturbation of Matrix Pairs: Hermite Indices *." IFAC Proceedings Volumes 37, no. 21 (2004): 49–54. http://dx.doi.org/10.1016/s1474-6670(17)30442-1.

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42

Stewart, G. W. "Perturbation theory for rectangular matrix pencils." Linear Algebra and its Applications 208-209 (September 1994): 297–301. http://dx.doi.org/10.1016/0024-3795(94)90445-6.

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43

Znojil, M. "Perturbation theory with band-matrix propagators." Physics Letters A 125, no. 9 (1987): 443–46. http://dx.doi.org/10.1016/0375-9601(87)90181-2.

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44

Duan, Xue-Feng, and Qing-Wen Wang. "Perturbation Analysis for the Matrix EquationX−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I." Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/784620.

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We consider the perturbation analysis of the matrix equationX−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I. Based on the matrix differentiation, we first give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the sharpness of the perturbation bound.

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45

Popchev, Ivan. "Why Perturbations?" Cybernetics and Information Technologies 20, no. 4 (2020): 170–75. http://dx.doi.org/10.2478/cait-2020-0054.

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AbstractReview on the book M. M. Konstantinov, P. H. Petkov. Perturbation Methods in Matrix Analysis and Control. NOVA Science Publishers, Inc., New York, 2020. ISBN 978-1-53617-470-0. https://novapublishers.com/shop/perturbation-methods-in-matrix-analysis-and-control/

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46

Farooq, Aamir, Mahvish Samar, Rewayat Khan, Hanyu Li, and Muhammad Kamran. "Perturbation analysis for the Takagi vector matrix." Special Matrices 10, no. 1 (2021): 23–33. http://dx.doi.org/10.1515/spma-2020-0144.

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Abstract In this article, we present some perturbation bounds for the Takagi vector matrix when the original matrix undergoes the additive or multiplicative perturbation. Two numerical examples are given to illuminate these bounds.

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47

Oprisan, Sorinel Adrian. "Local Linear Approximation of the Jacobian Matrix Better Captures Phase Resetting of Neural Limit Cycle Oscillators." Neural Computation 26, no. 1 (2014): 132–57. http://dx.doi.org/10.1162/neco_a_00536.

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One effect of any external perturbations, such as presynaptic inputs, received by limit cycle oscillators when they are part of larger neural networks is a transient change in their firing rate, or phase resetting. A brief external perturbation moves the figurative point outside the limit cycle, a geometric perturbation that we mapped into a transient change in the firing rate, or a temporal phase resetting. In order to gain a better qualitative understanding of the link between the geometry of the limit cycle and the phase resetting curve (PRC), we used a moving reference frame with one axis

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48

Rehman, Mutti-Ur, Jehad Alzabut, and Kamaleldin Abodayeh. "Computing Nearest Correlation Matrix via Low-Rank ODE’s Based Technique." Symmetry 12, no. 11 (2020): 1824. http://dx.doi.org/10.3390/sym12111824.

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For n-dimensional real-valued matrix A, the computation of nearest correlation matrix; that is, a symmetric, positive semi-definite, unit diagonal and off-diagonal entries between −1 and 1 is a problem that arises in the finance industry where the correlations exist between the stocks. The proposed methodology presented in this article computes the admissible perturbation matrix and a perturbation level to shift the negative spectrum of perturbed matrix to become non-negative or strictly positive. The solution to optimization problems constructs a gradient system of ordinary differential equat

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49

Adukov, Victor M., Gennady Mishuris, and Sergei V. Rogosin. "Exact conditions for preservation of the partial indices of a perturbed triangular 2 × 2 matrix function." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2237 (2020): 20200099. http://dx.doi.org/10.1098/rspa.2020.0099.

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The possible instability of partial indices is one of the important constraints in the creation of approximate methods for the factorization of matrix functions. This paper is devoted to a study of a specific class of triangular matrix functions given on the unit circle with a stable and unstable set of partial indices. Exact conditions are derived that guarantee a preservation of the unstable set of partial indices during a perturbation of a matrix within the class. Thus, even in this probably simplest of cases, when the factorization technique is well developed, the structure of the parametr

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Mitrophanov, Alexander Yu, Alexandre Lomsadze, and Mark Borodovsky. "Sensitivity of hidden Markov models." Journal of Applied Probability 42, no. 3 (2005): 632–42. http://dx.doi.org/10.1239/jap/1127322017.

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Abstract:

We derive a tight perturbation bound for hidden Markov models. Using this bound, we show that, in many cases, the distribution of a hidden Markov model is considerably more sensitive to perturbations in the emission probabilities than to perturbations in the transition probability matrix and the initial distribution of the underlying Markov chain. Our approach can also be used to assess the sensitivity of other stochastic models, such as mixture processes and semi-Markov processes.

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