Relevant bibliographies by topics / Singular M-matrix

Academic literature on the topic 'Singular M-matrix'

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Published: 10 March 2023

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Journal articles on the topic "Singular M-matrix"

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Montaño, Emedin, Mario Salas, and Ricardo L. Soto. "Nonnegativity Preservation under Singular Values Perturbation." Mathematical Problems in Engineering 2009 (2009): 1–25. http://dx.doi.org/10.1155/2009/301582.

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We study how singular values and singular vectors of a matrixAchange, under matrix perturbations of the formA+αuivi∗andA+αupvq∗,p≠q, whereα∈ℝ,Ais anm×npositive matrix with singular valuesσ1≥σ2≥⋯≥σr>0,r=min⁡{m,n}, anduj,vk, j=1,…,m;k=1,…,n, are the left and right singular vectors, respectively. In particular we give conditions under which this kind of perturbations preserve nonnegativity and certain matrix structures.
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Kaper, Hans G., and Allan M. Krall. "M(λ)-computation for singular differential systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 112, no. 3-4 (1989): 327–30. http://dx.doi.org/10.1017/s0308210500018783.

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SynopsisDepending upon the initial data associated with the fundamental matrix, the function M(λ), used to generate L2-solutions of homogeneous linear differential systems, may vary. We show that there is a matrix bilinear transformation between such functions M(λ) with different initial data and illustrate how the result can be used to simplify the calculation of a specific M(λ)-function for a scalar second-order problem.
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Keilson, J., and L. D. Servi. "The matrix M/M/∞ system: retrial models and Markov Modulated sources." Advances in Applied Probability 25, no. 2 (June 1993): 453–71. http://dx.doi.org/10.2307/1427662.

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The matrix-geometric work of Neuts could be viewed as a matrix variant of M/M/1. A 2 × 2 matrix counterpart of Neuts for M/M/∞ is introduced, the stability conditions are identified, and the ergodic solution is solved analytically in terms of the ten parameters that define it. For several cases of interest, system properties can be found from simple analytical expressions or after easy numerical evaluation of Kummer functions. When the matrix of service rates is singular, a qualitatively different solution is derived. Applications to telecommunications include some retrial models and an M/M/∞ queue with Markov-modulated input.
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Keilson, J., and L. D. Servi. "The matrix M/M/∞ system: retrial models and Markov Modulated sources." Advances in Applied Probability 25, no. 02 (June 1993): 453–71. http://dx.doi.org/10.1017/s0001867800025441.

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The matrix-geometric work of Neuts could be viewed as a matrix variant of M/M/1. A 2 × 2 matrix counterpart of Neuts for M/M/∞ is introduced, the stability conditions are identified, and the ergodic solution is solved analytically in terms of the ten parameters that define it. For several cases of interest, system properties can be found from simple analytical expressions or after easy numerical evaluation of Kummer functions. When the matrix of service rates is singular, a qualitatively different solution is derived. Applications to telecommunications include some retrial models and an M/M/∞ queue with Markov-modulated input.
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Li, Ren-cang, Wei-chao Wang, and Wei-guo Wang. "Deflating irreducible singular M-matrix algebraic Riccati equations." Numerical Algebra, Control and Optimization 3, no. 3 (July 2013): 491–518. http://dx.doi.org/10.3934/naco.2013.3.491.

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Ding, Xiucai. "Singular vector distribution of sample covariance matrices." Advances in Applied Probability 51, no. 01 (March 2019): 236–67. http://dx.doi.org/10.1017/apr.2019.10.

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AbstractWe consider a class of sample covariance matrices of the form Q = TXX*T*, where X = (xij) is an M×N rectangular matrix consisting of independent and identically distributed entries, and T is a deterministic matrix such that T*T is diagonal. Assuming that M is comparable to N, we prove that the distribution of the components of the right singular vectors close to the edge singular values agrees with that of Gaussian ensembles provided the first two moments of xij coincide with the Gaussian random variables. For the right singular vectors associated with the bulk singular values, the same conclusion holds if the first four moments of xij match those of the Gaussian random variables. Similar results hold for the left singular vectors if we further assume that T is diagonal.
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Bendito, E., A. Carmona, A. M. Encinas, and M. Mitjana. "The M-matrix inverse problem for singular and symmetric Jacobi matrices." Linear Algebra and its Applications 436, no. 5 (March 2012): 1090–98. http://dx.doi.org/10.1016/j.laa.2011.06.044.

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Cantó, Rafael, and Joan-Josep Climent. "Singular graph and extension of jordan chains of an M-Matrix." Linear Algebra and its Applications 241-243 (July 1996): 167–89. http://dx.doi.org/10.1016/0024-3795(95)00584-6.

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Truhar, Ninoslav, and Maja Petrač. "Damping Optimization of Linear Vibrational Systems with a Singular Mass Matrix." Mathematics 10, no. 11 (May 28, 2022): 1854. http://dx.doi.org/10.3390/math10111854.

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We present two novel results for small damped oscillations described by the vector differential equation Mx¨+Cx˙+Kx=0, where the mass matrix M can be singular, but standard deflation techniques cannot be applied. The first result is a novel formula for the solution X of the Lyapunov equation ATX+XA=−I, where A=A(v) is obtained from M,C(v)∈Rn×n, and K∈Rn×n, which are the so-called mass, damping, and stiffness matrices, respectively, and rank(M)=n−1. Here, C(v) is positive semidefinite with rank(C(v))=1. Using the obtained formula, we propose a very efficient way to compute the optimal damping matrix. The second result was obtained for a different structure, where we assume that dim(N(M))≥1 and internal damping exists (usually a small percentage of the critical damping). For this structure, we introduce a novel linearization, i.e., a novel construction of the matrix A in the Lyapunov equation ATX+XA=−I, and a novel optimization process. The proposed optimization process computes the optimal damping C(v) that minimizes a function v↦trace(ZX) (where Z is a chosen symmetric positive semidefinite matrix) using the approximation function g(v)=cv+av+bv, for the trace function f(v)≐trace(ZX(v)). Both results are illustrated with several corresponding numerical examples.
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Barlow, Jesse L. "On the Smallest Positive Singular Value of a Singular M-Matrix with Applications to Ergodic Markov Chains." SIAM Journal on Algebraic Discrete Methods 7, no. 3 (July 1986): 414–24. http://dx.doi.org/10.1137/0607047.

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Dissertations / Theses on the topic "Singular M-matrix"

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Addis, Elena. "Elementwise accurate algorithms for nonsymmetric algebraic Riccati equations associated with M-matrices." Doctoral thesis, 2022. http://hdl.handle.net/2158/1275470.

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We present an elementwise accurate algorithm which incorporates the shift technique for the computation of the minimal non negative solution of a nonsymmetric algebraic Riccati equation associated to M, when M is an irreducible singular M-matrix. We propose the idea of delayed shift and some results that guarantees the applicability and the convergence of structured doubling algorithm based only on the properties of the matrix of the initial setup of doubling algorithm instead of matrix M. We provide a componentwise error analysis for the algorithm and we also show some numerical experiments that illustrate the advantage in terms of accuracy and convergence speed.
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Books on the topic "Singular M-matrix"

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Bouchaud, Jean-Philippe. Random matrix theory and (big) data analysis. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0006.

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This chapter reviews methods from random matrix theory to extract information about a large signal matrix C (for example, a correlation matrix arising in big data problems), from its noisy observation matrix M. The chapter shows that the replica method can be used to obtain both the spectral density and the overlaps between noise-corrupted eigenvectors and the true ones, for both additive and multiplicative noise. This allows one to construct optimal rotationally invariant estimators of C based on the observation of M alone. This chapter also discusses the case of rectangular correlation matrices and the problem of random singular value decomposition.
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Conference papers on the topic "Singular M-matrix"

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Xu, Yong-Xian, Dilip Kohli, and Tzu-Chen Weng. "Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0199.

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Abstract A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulations leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.
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Xiao, Yichi, Zhe Li, Tianbao Yang, and Lijun Zhang. "SVD-free Convex-Concave Approaches for Nuclear Norm Regularization." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/436.

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Minimizing a convex function of matrices regularized by the nuclear norm arises in many applications such as collaborative filtering and multi-task learning. In this paper, we study the general setting where the convex function could be non-smooth. When the size of the data matrix, denoted by m x n, is very large, existing optimization methods are inefficient because in each iteration, they need to perform a singular value decomposition (SVD) which takes O(m^2 n) time. To reduce the computation cost, we exploit the dual characterization of the nuclear norm to introduce a convex-concave optimization problem and design a subgradient-based algorithm without performing SVD. In each iteration, the proposed algorithm only computes the largest singular vector, reducing the time complexity from O(m^2 n) to O(mn). To the best of our knowledge, this is the first SVD-free convex optimization approach for nuclear-norm regularized problems that does not rely on the smoothness assumption. Theoretical analysis shows that the proposed algorithm converges at an optimal O(1/\sqrt{T}) rate where T is the number of iterations. We also extend our algorithm to the stochastic case where only stochastic subgradients of the convex function are available and a special case that contains an additional non-smooth regularizer (e.g., L1 norm regularizer). We conduct experiments on robust low-rank matrix approximation and link prediction to demonstrate the efficiency of our algorithms.
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Mu¨ller, Andreas, and Timo Hufnagel. "Adaptive and Singularity-Free Inverse Dynamics Models for Control of Parallel Manipulators With Actuation Redundancy." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47943.

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Redundant actuation of parallel kinematics machines (PKM) is a way to eliminate input-singularities and so to enlarge the usable workspace. From a kinematic point of view the number m of actuator coordinates exceeds the DOF δ of a redundantly actuated PKM (RA-PKM). The dynamics model, being the basis for model-based control, is usually expressed in terms of δ independent actuator coordinates. This implies that the model exhibits the same singularities as the non-redundant PKM, even though the RA-PKM is not singular. Consequently the admissible range of motion of the RA-PKM model is limited to that of the non-redundant PKM. In this paper an alternative formulation of the dynamics model in terms of the full set of m actuator coordinates is presented. It leads to a redundant system of m motion equations that is valid in the entire range of motion. This formulation gives rise to an inverse dynamics formulation tailored for real-time implementation. In contrast to the standard formulation in independent coordinates, the proposed inverse dynamics formulation does not involve control forces in the null space of the control matrix, i.e. it does not allow for the generation of internal prestresses, however. This is not problematic as the latter is usually not exploited. The proposed method is compared to the recently proposed adaptive coordinate switching method. Experimental results are reported if the inverse dynamics solution is introduced in model-based computed torque control scheme of a planar 2DOF RA-PKM.
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