Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. We present three original deterministic and stochastic iterative algorithms for optimal ...
详细信息
Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. We present three original deterministic and stochastic iterative algorithms for optimal state estimation of JMLS whose computational complexity at each iteration is linear in the data length. The first algorithm yields conditional mean estimates. The second algorithm is an algorithm that yields the marginal maximum a posteriori (MMAP) sequence estimate of the finite state Markov chain. The third algorithm is an algorithm that yields the MMAP sequence estimate of the continuous state of the JMLS. Convergence results for these three algorithms are obtained. Computer simulations are carried out to evaluate their performance.
We propose some iterative algorithms for the generation of open-loop controls of quantum systems. The task that these controls are intended for is the transfer of a given initial state to a given final state with maxi...
详细信息
We propose some iterative algorithms for the generation of open-loop controls of quantum systems. The task that these controls are intended for is the transfer of a given initial state to a given final state with maximal probability. We prove that the algorithms are converging and the resulting controls are optimal.
The TOF clinical data are very sparse and have significant size. These data undergo TOF axial rebinning and azimuthal mashing if histogrammed data-based reconstruction algorithms are used. In a clinical environment, T...
详细信息
The TOF clinical data are very sparse and have significant size. These data undergo TOF axial rebinning and azimuthal mashing if histogrammed data-based reconstruction algorithms are used. In a clinical environment, TOF compression is performed by the hardware rebinner. Normalization data, acquired on a regular basis and used for estimation of some norm components, are compressed by the hardware rebinner in a similar manner. In this paper we present simple update iterative algorithms for crystal efficiencies norm component estimation from TOF compressed normalization data. The previously known methods are not directly applicable, since the compression procedure significantly complicates normalization data model equations. Presented iterative methods have the advantages of easy adaptation to any acquisition geometry, and of allowing the estimation of parameters at the crystal level when the number of crystals is relatively small. A monotonic sequential coordinate descent algorithm, which optimizes the Least Squares objective function, is investigated. A simultaneous update algorithm, which possesses the advantage of easy parallelization, is also derived. Measured normalization data from a Siemens prototype TOF scanner are used to validate the algorithms performance.
The authors discuss a series of numerical experiments, aiming at the comparison of several iterative algorithms designed to reconstruct band-limited signals from irregularly spaced samples. The authors give a short de...
详细信息
The authors discuss a series of numerical experiments, aiming at the comparison of several iterative algorithms designed to reconstruct band-limited signals from irregularly spaced samples. The authors give a short description of these algorithms and then discuss possible criteria for the quality or performance of these algorithms. It turns out that appropriate criteria for such an evaluation are more involved than one might think from the literature. Among the properties discussed are various notions of speed, measures of the stability of the reconstruction algorithms and the range in which complete reconstruction is performed. The authors concentrate on the representation of the one-dimensional problems, although the underlying theory has been developed for several dimensions. Only qualitative statements are given.< >
We present two finite dimensional iterative algorithms for maximum a posteriori (MAP) state sequence estimation of bilinear systems. The novel idea is to use the expectation maximization (EM) algorithm for state estim...
详细信息
We present two finite dimensional iterative algorithms for maximum a posteriori (MAP) state sequence estimation of bilinear systems. The novel idea is to use the expectation maximization (EM) algorithm for state estimation rather than the traditional maximum likelihood parameter estimation. We present the EM-I and EM-II algorithms.
iterative algorithms are useful for retrieving wavefront phase from vibration disturbed interferograms for phase-shifting interferometry (PSI). But the dependence of convergence on the initial value deviation from the...
详细信息
iterative algorithms are useful for retrieving wavefront phase from vibration disturbed interferograms for phase-shifting interferometry (PSI). But the dependence of convergence on the initial value deviation from the exact value impairs their application in severe vibration. In this paper, performance investigation of a representative iterative algorithm indicates that a higher frame rate of the camera, with matched phase shift, helps in enhancing the success probability of convergence. However, the camera frame rate is limited by its transmission speed and could not be increased easily. To improve the convergence of iterative algorithms, a dualmode (DM) PSI is proposed that utilises the binning function of cameras. In DMPSI, two modes, high-speed and high-resolution modes, work consecutively by switching the camera binning function and two series of interferograms are collected respectively. The wavefront phase could be accurately estimated from high-speed interferograms and then is input to the iterative calculation with high-resolution interferograms as the initial value, and a wavefront phase with high-resolution is achieved ultimately. DMPSI combines the advantages of two complementary modes of cameras to reconstruct an accurate and high-resolution wavefront. Both simulations and a practical measurement verify the enhancement of vibration resistance of iterative algorithms. DMPSI is easy to implement with low cost and good compatibility, predicating a reliable solution for optical wavefront measurement in the severe vibration.
iterative algorithms are widely applied in reliability analysis and design optimization. Nevertheless, phenomena of failed convergence, such as periodic oscillation, bifurcation, and chaos, are oftentimes observed in ...
详细信息
iterative algorithms are widely applied in reliability analysis and design optimization. Nevertheless, phenomena of failed convergence, such as periodic oscillation, bifurcation, and chaos, are oftentimes observed in iterative procedures of solving some nonlinear problems. In the present paper, the essential causes of numerical instabilities including periodic oscillation and chaos of iterative solutions are revealed by the eigenvalue-based stability analysis of iterative schemes. To understand and control these instabilities, the stability transformation method (STM), which is capable of tackling numerical instabilities of iterative algorithms in reliability analysis and design optimization, is proposed. Finally, several benchmark examples of convergence control of PMA (performance measure approach) for probabilistic analysis and the SORA (sequential optimization and reliability assessment) for reliability-based design optimization (RBDO) are presented. The observations from the benchmark examples indicate that the STM is a promising approach to achieve convergence control for iterative algorithms in reliability analysis and design optimization.
This paper discusses identification of the fractional order Hammerstein model with colored noise. The static part of the Hammerstein model is a two-stage piecewise nonlinearity, while the dynamic part is a CARMA struc...
详细信息
This paper discusses identification of the fractional order Hammerstein model with colored noise. The static part of the Hammerstein model is a two-stage piecewise nonlinearity, while the dynamic part is a CARMA structure. We deduce the identification expression of the model through the definition of the Grunwald- Letnikov fractional differential. Then, two iterative algorithms are adopted to identify the unknown parameters. One of them is the Levenberg-Marquardt iterative algorithm, and the other is the particle swarm optimization iterative algorithm. The two algorithms are extended from the traditional integer order system identification field to the fractional order nonlinear colored noise system identification field. A numerical example and a case study of servo system identification are respectively presented to demonstrate the feasibility of the identification algorithms. It can be seen that the estimation errors of these two algorithms are relatively small, which reflects their good identification effect.
In the framework of steady-state inhomogeneous anisotropic heat conduction with heat sources, we study the convergent and stable numerical reconstruction of the missing boundary conditions (temperatures and normal hea...
详细信息
In the framework of steady-state inhomogeneous anisotropic heat conduction with heat sources, we study the convergent and stable numerical reconstruction of the missing boundary conditions (temperatures and normal heat fluxes) on an inaccessible boundary and the thermal field in a 2D solid from the knowledge of over-prescribed data on an accessible portion of the boundary and temperature data on the remaining boundary. This inverse boundary value problem is approached by employing the alternating iterative algorithms of Kozlov et al. (1991), in conjunction with the standard finite-difference method and a novel modified one, for both exact and perturbed data. For noisy data available on the over-prescribed boundary, the numerical solution is retrieved by using three regularising/stabilising stopping criteria. Numerical results are presented for 2D simply and doubly connected domains bounded by a (piecewise) smooth curve, as well as exact and noisy boundary data, whilst appropriate errors in the fractional Sobolev spaces corresponding to the boundary temperatures and normal heat fluxes, respectively, are computed efficiently.
Many iterative algorithms, for example the BCG algorithm, the CGS algorithm etc., for solving nonsymmetric linear systems have the erratic convergence behavior. Recently, Freund et al. [6] proposed a BCG-like approach...
详细信息
Many iterative algorithms, for example the BCG algorithm, the CGS algorithm etc., for solving nonsymmetric linear systems have the erratic convergence behavior. Recently, Freund et al. [6] proposed a BCG-like approach, the Quasi-minimal residual (QMR) method, that remedies this problem for BCG and produces smooth convergence curves. The QMR approach is also applied to CGS and BI-CGSTAB to obtain smoothly convergent variants of these algorithms [7, 5, 12]. In this paper, we propose a simple but universal QMR approach which can be applied with unified manner to any iterative algorithm to construct smoothly convergent variants, provided this algorithm includes two-term recurrence for the approximate solutions. The resulting QMR algorithms can be implemented very easily by changing only a few lines in the original iterative algorithm. We compare the performance of our QMR approach with that of other QMR methods presented in [5], [7] and [12]. Finally, numerical examples are given.
暂无评论