Relevant bibliographies by topics / Minimal nonnegative solution

Academic literature on the topic 'Minimal nonnegative solution'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Minimal nonnegative solution"

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Guo, Pei-Chang. "Newton-Shamanskii Method for a Quadratic Matrix Equation Arising in Quasi-Birth-Death Problems." East Asian Journal on Applied Mathematics 4, no. 4 (November 2014): 386–95. http://dx.doi.org/10.4208/eajam.040914.301014a.

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AbstractIn order to determine the stationary distribution for discrete time quasi-birth-death Markov chains, it is necessary to find the minimal nonnegative solution of a quadratic matrix equation. The Newton-Shamanskii method is applied to solve this equation, and the sequence of matrices produced is monotonically increasing and converges to its minimal nonnegative solution. Numerical results illustrate the effectiveness of this procedure.
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Guo, Pei-Chang. "A Fast Newton-Shamanskii Iteration for a Matrix Equation Arising from M/G/1-Type Markov Chains." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/4018239.

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For the nonlinear matrix equations arising in the analysis of M/G/1-type and GI/M/1-type Markov chains, the minimal nonnegative solution G or R can be found by Newton-like methods. We prove monotone convergence results for the Newton-Shamanskii iteration for this class of equations. Starting with zero initial guess or some other suitable initial guess, the Newton-Shamanskii iteration provides a monotonically increasing sequence of nonnegative matrices converging to the minimal nonnegative solution. A Schur decomposition method is used to accelerate the Newton-Shamanskii iteration. Numerical examples illustrate the effectiveness of the Newton-Shamanskii iteration.
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Garić-Demirović, M., M. R. S. Kulenović, and M. Nurkanović. "Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation." Scientific World Journal 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/210846.

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We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the formxn+1=xn-12/(axn2+bxnxn-1+cxn-12),n=0,1,2,…,where the parameters a, b, and c are positive numbers and the initial conditionsx-1andx0are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable.
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Ivanov, Ivan G. "ITERATIVE COMPUTING THE MINIMAL SOLUTION OF THE COUPLED NONLINEAR MATRIX EQUATIONS IN TERMS OF NONNEGATIVE MATRICES." Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application 12, no. 1-2 (2020): 226–37. http://dx.doi.org/10.56082/annalsarscimath.2020.1-2.226.

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We investigate a set of nonlinear matrix equations with nonnegative matrix coefficients which has arisen in applied sciences. There are papers where the minimal nonnegative solution of the set of nonlinear matrix equations is computed applying the different procedures. The alternate linear implicit method and its modifications have intensively investigated because they have simple computational scheme. We construct a new decoupled modification of the alternate linear implicit procedure to compute the minimal nonnegative solution of the considered set of equations. The convergence properties of the proposed iteration are derived and a sufficient condition for convergence is derived. The performance of the proposed algorithm is illustrated on several numerical examples. On the basis of the experiments we derive conclusions for applicability of the computational schemes.
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Hammoudi, Alaaeddine, Oana Iosifescu, and Martial Bernoux. "Mathematical analysis of a spatially distributed soil carbon dynamics model." Analysis and Applications 15, no. 06 (August 2, 2017): 771–93. http://dx.doi.org/10.1142/s0219530516500081.

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The aim of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction–diffusion–advection system with a quadratic reaction term. This is a spatial version of Modeling Organic changes by Micro-Organisms of Soil model, recently introduced by M. Pansu and his group. We show here that for any nonnegative initial condition, there exists a unique nonnegative weak solution. Moreover, if we assume time periodicity of model entries, taking into account seasonal effects, we prove existence of a minimal and a maximal periodic weak solution. In a particular case, these two solutions coincide and they become a global attractor of any bounded solution of the periodic system.
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Zhang, Xuemei, Xiaozhong Yang, and Meiqiang Feng. "Minimal Nonnegative Solution of Nonlinear Impulsive Differential Equations on Infinite Interval." Boundary Value Problems 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/684542.

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Ivanshin, Pyotr. "Functions of Minimal Norm with the Given Set of Fourier Coefficients." Mathematics 7, no. 7 (July 20, 2019): 651. http://dx.doi.org/10.3390/math7070651.

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We prove the existence and uniqueness of the solution of the problem of the minimum norm function ∥ · ∥ ∞ with a given set of initial coefficients of the trigonometric Fourier series c j , j = 0 , 1 , … , 2 n . Then, we prove the existence and uniqueness of the solution of the nonnegative function problem with a given set of coefficients of the trigonometric Fourier series c j , j = 1 , … , 2 n for the norm ∥ · ∥ 1 .
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Guo, Chun-Hua. "A note on the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation." Linear Algebra and its Applications 357, no. 1-3 (December 2002): 299–302. http://dx.doi.org/10.1016/s0024-3795(02)00431-7.

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Zhang, Lihong, Bashir Ahmad, and Guotao Wang. "Monotone iterative method for a class of nonlinear fractional differential equations on unbounded domains in Banach spaces." Filomat 31, no. 5 (2017): 1331–38. http://dx.doi.org/10.2298/fil1705331z.

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In this paper, we investigate the existence of minimal nonnegative solution for a class of nonlinear fractional integro-differential equations on semi-infinite intervals in Banach spaces by applying the cone theory and the monotone iterative technique. An example is given for the illustration of main results.
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Miyajima, Shinya. "Fast verified computation for the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation." Computational and Applied Mathematics 37, no. 4 (February 13, 2018): 4599–610. http://dx.doi.org/10.1007/s40314-018-0590-x.

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Dissertations / Theses on the topic "Minimal nonnegative solution"

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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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Book chapters on the topic "Minimal nonnegative solution"

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Bakonyi, Mihály, and Hugo J. Woerdeman. "Hermitian and related completion problems." In Matrix Completions, Moments, and Sums of Hermitian Squares. Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691128894.003.0005.

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This chapter considers various completion problems that are in one way or another closely related to positive semidefinite or contractive completion problems. For instance, as a variation on requiring that all eigenvalues of the completion are positive/nonnegative, one can consider the question how many eigenvalues of a Hermitian completion have to be positive/nonnegative. In the solution to the latter problem ranks of off-diagonal parts will play a role, which is why minimal rank completions are also discussed. Related is a question on real measures on the real line. As a variation of the contractive completion problem, the chapter considers the question how many singular values of a completion have to be smaller (or larger) than one. It also looks at completions in classes of normal matrices and distance matrices. As applications it turns to questions regarding Hermitian matrix expressions, a minimal representation problem for discrete systems, and the separability problem that appears in quantum information. Exercises and notes are provided at the end of the chapter.
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Conference papers on the topic "Minimal nonnegative solution"

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Fabien, Brian C. "A Simple Continuation Method for the Solution of Optimal Control Problems With State Variable Inequality Constraints." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13617.

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This paper develops a simple continuation method for the approximate solution of optimal control problems with pure state variable inequality constraints. The method is based on transforming the inequality constraints into equality constraints using nonnegative slack variables. The resultant equality constraints are satisfied approximately using a quadratic loss penalty function. The solution of the original problem is obtained by solving the transformed problem with a sequence of penalty weights that tends to zero. The penalty weight is treated as the continuation parameter. The necessary conditions for a minimum are written as a boundary value problem involving index-1 differential-algebraic equations (BVP-DAE). The BVP-DAE include the complementarity conditions associated with the inequality constraints. The paper shows that the necessary conditions for optimality of the original problem and the transformed problems are remarkably similar. In particular, the BVP-DAE for each problem differ by a linear term related to the Lagrange multipliers associated with the state variable inequality constraints. Numerical examples are presented to illustrate the efficacy of the proposed technique. Specifically, the paper presents results for; (1) the optimal control of a simplified model of a gantry crane system, (2) the optimal control of a rigid body moving in the vertical plane, and (3) the trajectory optimization of a planar two-link robot. All problems include pure state variable inequality constraints.
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Liu, Kai, and Hua Wang. "High-Order Co-Clustering via Strictly Orthogonal and Symmetric L1-Norm Nonnegative Matrix Tri-Factorization." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/340.

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Different to traditional clustering methods that deal with one single type of data, High-Order Co- Clustering (HOCC) aims to cluster multiple types of data simultaneously by utilizing the inter- or/and intra-type relationships across different data types. In existing HOCC methods, data points routinely enter the objective functions with squared residual errors. As a result, outlying data samples can dominate the objective functions, which may lead to incorrect clustering results. Moreover, existing methods usually suffer from soft clustering, where the probabilities to different groups can be very close. In this paper, we propose an L1 -norm symmetric nonnegative matrix tri-factorization method to solve the HOCC problem. Due to the orthogonal constraints and the symmetric L1 -norm formulation in our new objective, conventional auxiliary function approach no longer works. Thus we derive the solution algorithm using the alternating direction method of multipliers. Extensive experiments have been conducted on a real world data set, in which promising empirical results, including less time consumption, strictly orthogonal membership matrix, lower local minima etc., have demonstrated the effectiveness of our proposed method.
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