This paper analyzes the performance of the orthogonal matching pursuit （OMP） algorithm in recovering sparse signals from noisy measurement. Considering the fact that some matrices satisfy some restricted isometry pr...This paper analyzes the performance of the orthogonal matching pursuit （OMP） algorithm in recovering sparse signals from noisy measurement. Considering the fact that some matrices satisfy some restricted isometry properties （RIPs） but not the coherence condition, a superior RIP-based condition is proposed, which means that if the measurement matrix satisfies δk＋1 〈 1/（2 ＋ √k） and the minimum component signal-to-noise ratio （MCSNR） is bounded, the OMP algorithm can exactly identify the support of the original sparse signal within k iterations. Finally, the theoretical results are verified by numerical simulations con- cerning different values of MCSNR and noise levels.展开更多
In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradien...In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient method.Under the condition of standard Wolfe line search,the proposed search direction is the descent direction.For general nonlinear functions,the method is globally convergent.Finally,numerical results show that the proposed method is efficient.展开更多
The sufficient conditions of stability for uncertain discrete-time systems with state delay have been proposed by some researchers in the past few years, yet these results may be conservative in application. The stabi...The sufficient conditions of stability for uncertain discrete-time systems with state delay have been proposed by some researchers in the past few years, yet these results may be conservative in application. The stability analysis of these systems is discussed, and the necessary and sufficient condition of stability is derived by method other than constructing Lyapunov function and solving Riccati inequality. The root locations of system characteristic polynomial, which is obtained by augmentation approach and Laplace expansion, determine the stability of uncertain discrete-time systems with state delay, the system is stable if and only if all roots lie within the unit circle. In order to analyze robust stability of system characteristic polynomial effectively, Kharitonov theorem and edge theorem are applied. Example shows the practicability of these methods.展开更多
In this paper, with the Kronecker's product and Kronecker's sum of matrices, the 2nd order moment equations of linear Ito stochastic systems are dervided. Based on the moment equations obtained, a necessary an...In this paper, with the Kronecker's product and Kronecker's sum of matrices, the 2nd order moment equations of linear Ito stochastic systems are dervided. Based on the moment equations obtained, a necessary and sufficient condition for the mean-square asymptotic stability of linear Ito stochastic systems is obtained.For the time-invariant stochastic systems,the necessary and sufficient condition is just the same as the Hurwitz property of certain matrices related to the coefficient matrices of the systems. An algorithm STILSS is given for testing the mean-square asymptotic stability of time-invariant linear Ito stochastic systems.展开更多
基金supported by the National Natural Science Foundation of China(6117401661171197)
文摘This paper analyzes the performance of the orthogonal matching pursuit （OMP） algorithm in recovering sparse signals from noisy measurement. Considering the fact that some matrices satisfy some restricted isometry properties （RIPs） but not the coherence condition, a superior RIP-based condition is proposed, which means that if the measurement matrix satisfies δk＋1 〈 1/（2 ＋ √k） and the minimum component signal-to-noise ratio （MCSNR） is bounded, the OMP algorithm can exactly identify the support of the original sparse signal within k iterations. Finally, the theoretical results are verified by numerical simulations con- cerning different values of MCSNR and noise levels.
基金Supported by the Science and Technology Project of Guangxi(Guike AD23023002)。
文摘In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient method.Under the condition of standard Wolfe line search,the proposed search direction is the descent direction.For general nonlinear functions,the method is globally convergent.Finally,numerical results show that the proposed method is efficient.
基金This project was supported by National "863" High Technology Research and Development Program of China (2001-AA413130) and the National Key Research Project (2001-BA201A04).
文摘The sufficient conditions of stability for uncertain discrete-time systems with state delay have been proposed by some researchers in the past few years, yet these results may be conservative in application. The stability analysis of these systems is discussed, and the necessary and sufficient condition of stability is derived by method other than constructing Lyapunov function and solving Riccati inequality. The root locations of system characteristic polynomial, which is obtained by augmentation approach and Laplace expansion, determine the stability of uncertain discrete-time systems with state delay, the system is stable if and only if all roots lie within the unit circle. In order to analyze robust stability of system characteristic polynomial effectively, Kharitonov theorem and edge theorem are applied. Example shows the practicability of these methods.
文摘In this paper, with the Kronecker's product and Kronecker's sum of matrices, the 2nd order moment equations of linear Ito stochastic systems are dervided. Based on the moment equations obtained, a necessary and sufficient condition for the mean-square asymptotic stability of linear Ito stochastic systems is obtained.For the time-invariant stochastic systems,the necessary and sufficient condition is just the same as the Hurwitz property of certain matrices related to the coefficient matrices of the systems. An algorithm STILSS is given for testing the mean-square asymptotic stability of time-invariant linear Ito stochastic systems.
