M-matrix Related Publications
6 Convergence and Comparison Theorems of the Modified Gauss-Seidel Method
Authors: Zhouji Chen
Abstract:
In this paper, the modified Gauss-Seidel method with the new preconditioner for solving the linear system Ax = b, where A is a nonsingular M-matrix with unit diagonal, is considered. The convergence property and the comparison theorems of the proposed method are established. Two examples are given to show the efficiency and effectiveness of the modified Gauss-Seidel method with the presented new preconditioner.
Keywords: Convergence, M-matrix, comparison theorem, Preconditioned linear system
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12495 Bi-linear Complementarity Problem
Authors: Chao Wang, Ting-Zhu Huang Chen Jia
Abstract:
In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.
Keywords: M-matrix, Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P-matrix
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13904 Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices
Authors: Jing Li, Guang Zhou
Abstract:
Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.
Keywords: hadamard product, M-matrix, spectral radius, Fan product; nonnegative matrix, Minimum eigenvalue
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16033 Preconditioned Jacobi Method for Fuzzy Linear Systems
Authors: Lina Yan, Shiheng Wang, Ke Wang
Abstract:
A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.
Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS)
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16142 Existence and Global Exponential Stability of Periodic Solutions of Cellular Neural Networks with Distributed Delays and Impulses on Time Scales
Authors: Daiming Wang
Abstract:
In this paper, by using Mawhin-s continuation theorem of coincidence degree and a method based on delay differential inequality, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of cellular neural networks with distributed delays and impulses on time scales. The results of this paper generalized previously known results.
Keywords: Periodic solutions, coincidence degree, Global exponential stability, M-matrix
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11361 Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching
Authors: Xia Zhou, Shouming Zhong
Abstract:
The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.
Keywords: Synchronization, Markov Chain, Brownian motion, M-matrix, delay-range-dependent, generalized Itō's formula
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1240