This paper proposes a novel method of using the frequency-domain transfer function to investigate the property of an iterative algorithm for minimizing a quadratic objective function. This paper focuses on a 2-D tomog...
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This paper proposes a novel method of using the frequency-domain transfer function to investigate the property of an iterative algorithm for minimizing a quadratic objective function. This paper focuses on a 2-D tomography problem, which can be X-ray computed tomography (CT), positron emission tomography, and single photon emission CT. Two questions regarding to the linear iterative Landweber algorithm are considered. The first question is whether stopping early is equivalent to getting a minimum-norm solution. The second question is whether the low frequency components always converge first. Our answers to these two questions are No.
Algebraic Riccati matrix equations arise naturally in various situations and their role and application in systems, filtering, stochastic process, and control theory, in particular, have been well established in recen...
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Algebraic Riccati matrix equations arise naturally in various situations and their role and application in systems, filtering, stochastic process, and control theory, in particular, have been well established in recent years. This study presents iterative algorithms to solve the algebraic Riccati matrix equation (ARME) R( X) = XDX - XC - BX + A = 0, based on the weight splitting (WS). We demonstrate that the iterative algorithms converge to non-positive and non-negative solutions of the ARME in special situations. To compare the newalgorithms with the previously existing algorithm, we present some numerical examples.
To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and dee...
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To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network defined on the whole problem domain. In such a partitioned neural network approach, suitable interface conditions or subdomain boundary conditions are combined to obtain a convergent approximate solution. However, there has been no rigorous study on the convergence and parallel computing enhancement on the partitioned neural network approach. In this paper, iterative algorithms are proposed to enhance parallel computation performance in the partitioned neural network approximation. Our iterative algorithms are based on classical additive Schwarz domain decomposition methods. For the proposed iterative algorithms, their convergence is analyzed under an error assumption on the local and coarse neural network solutions. Numerical results are also included to show the performance of the proposed iterative algorithms.
Plenoptic imaging is a revolutionary photographic technique which has been brought to public awareness recently. It makes post-refocusing possible by capturing both spatial and directional information of light. In ord...
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Plenoptic imaging is a revolutionary photographic technique which has been brought to public awareness recently. It makes post-refocusing possible by capturing both spatial and directional information of light. In order to do that, a micro-lens is placed before the imaging plane of the camera. Each micro-lens records angular information from its location at the cost of spatial resolution. A focal stack is generated by stacking up refocused images of the same object. By adjusting the depth at which each image focuses, it models the light ray around the nominal focal plane of the camera in 3D. The main purpose of this thesis is to reconstruct the surface based on focal stacks. There were previous attempts to accomplish the same task, including the gradient method and the stereo method; however, they are unable to reconstruct a smooth object. Later research proposed a deconvolution method that can address the smooth object problem. The thesis demonstrates the limitation of the deconvolution method and proposes an iterative method to more precisely reconstruct the surface of the object. In order to implement the iterative algorithm, the thesis also mathematically models the process of image blur as the vectorized object multiplied with a convolution matrix which represents the point-spread function (PSF). The PSF describes the spread of light from the object across the entire focal stack. Various results of estimating depth from different methods are presented to compare the performance of each algorithm.
In this paper, hybrid technique proposed for tuning Time Delays System with proportional-integral-derivative (PID) controller. So, the performance and the robustness for a class of Time Delay System are improved. The ...
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In this paper, hybrid technique proposed for tuning Time Delays System with proportional-integral-derivative (PID) controller. So, the performance and the robustness for a class of Time Delay System are improved. The proposed hybrid technique is the combination of the iterative algorithm and curve fitting technique. The proposed iterative algorithm is improved, performance of the feedback tuning iterative technique;so the computational complexity of the iterative algorithm reduced. By using the iterative technique, the best polynomial coefficients of curve fitting technique is determined. Using the curve fitting technique, the Time Delay System is tuned and the stability parameters of the system is maintained. The curve fitting technique is one of the non linear programming techniques which can be constructed that approximately fits the data from the extract data. The proposed hybrid technique is implemented in MATLAB working platform and the tuning performance is evaluated. Then, the system performance of the proposed hybrid technique is compared with classical PID controller, Ziegler-Nichols tuning method.
Background: The management of genetic variation in a breeding scheme relies very much on the control of the average relationship between selected parents. Optimum contribution selection is a method that seeks the opti...
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Background: The management of genetic variation in a breeding scheme relies very much on the control of the average relationship between selected parents. Optimum contribution selection is a method that seeks the optimum way to select for genetic improvement while controlling the rate of inbreeding. Methods: A novel iterative algorithm, Gencont2, for calculating optimum genetic contributions was developed. It was validated by comparing it with a previous program, Gencont, on three datasets that were obtained from practical breeding programs in three species (cattle, pig and sheep). The number of selection candidates was 2929, 3907 and 6875 for the pig, cattle and sheep datasets, respectively. Results: In most cases, both algorithms selected the same candidates and led to very similar results with respect to genetic gain for the cattle and pig datasets. In cases, where the number of animals to select varied, the contributions of the additional selected candidates ranged from 0.006 to 0.08 %. The correlations between assigned contributions were very close to 1 in all cases;however, the iterative algorithm decreased the computation time considerably by 90 to 93 % (13 to 22 times faster) compared to Gencont. For the sheep dataset, only results from the iterative algorithm are reported because Gencont could not handle a large number of selection candidates. Conclusions: Thus, the new iterative algorithm provides an interesting alternative for the practical implementation of optimal contribution selection on a large scale in order to manage inbreeding and increase the sustainability of animal breeding programs.
Mean first passage times are an essential ingredient in both the theory and the applications of Markov chains. In the literature, they have been expressed in elegant closed-form formulas. These formulas involve explic...
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Mean first passage times are an essential ingredient in both the theory and the applications of Markov chains. In the literature, they have been expressed in elegant closed-form formulas. These formulas involve explicit full matrix inversions and, if computed directly, may incur numerical instability. In this paper, we present a new iterative algorithm for computing mean first passage times in a manner that does not rely on explicit full matrix inversions. Results regarding the convergence behavior of this algorithm are also developed. (C) 2014 Elsevier Inc. All rights reserved.
In this article, some convergence conditions are investigated for the multiple tuning parameters iterative algorithm (MIA) and the single tuning parameter iterative algorithm (SIA), which are proposed to solve the dis...
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In this article, some convergence conditions are investigated for the multiple tuning parameters iterative algorithm (MIA) and the single tuning parameter iterative algorithm (SIA), which are proposed to solve the discrete periodic Lyapunov matrix equations related to discrete-time linear periodic systems. First, when all the tuning parameters are selected in the interval (0, 1] and the initial conditions are arbitrarily given, it is proven that the MIA is convergent if and only if the discrete-time linear periodic system is asymptotically stable. In particular, when the coefficient matrices of the considered matrix equations are nonnegative, it is shown that the convergence rate of the MIA increases with the tuning parameter increases from 0 to 1. Moreover, the above convergence results derived for the MIA are extended to the SIA. Furthermore, the searching interval of the optimal tuning parameter for the SIA to achieve the fastest convergence rate is narrowed. Finally, two numerical examples are provided to demonstrate the correctiveness of the proposed theoretical results.
In this paper, we focus on the following coupled linear matrix equations M-i(X, Y) = M-i1(X) + M-i2(Y) = Li, with M-il(W) = (q)Sigma(j= 1) ( t(1)((l))Sigma(lambda=1) A(ij lambda)((l)) W-j B-ij lambda((l)) +t(2)((l))Si...
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In this paper, we focus on the following coupled linear matrix equations M-i(X, Y) = M-i1(X) + M-i2(Y) = Li, with M-il(W) = (q)Sigma(j= 1) ( t(1)((l))Sigma(lambda=1) A(ij lambda)((l)) W-j B-ij lambda((l)) +t(2)((l))Sigma(mu=1) C-ij lambda((l)) W-j D-ij lambda((l)) + t(3)((l))Sigma(lambda=1) E-ij lambda((l)) W-j B-j(T) F-ij lambda((l)) ) l=1,2 where A(ij lambda)((l)) B-ij lambda((l)) C-ij lambda j((l)) D-ij lambda((l)) E-ij lambda((l)) F-ij lambda((l)) and Li (for i is an element of I [1, p]) are given matrices with appropriate dimensions defined over complex number field. Our object is to obtain the solution groups X = (X-1, X-2,..., X-q) and Y = (Y-1, Y-2,..., Y-q) of the considered coupled linear matrix equations such that X and Y are the groups of the Hermitian reflexive and skew-Hermitian matrices, respectively. To do so, an iterative algorithm is proposed which stops within finite number of steps in the exact arithmetic. Moreover, the algorithm determines the solvability of the mentioned coupled linear matrix equations over the Hermitian reflexive and skew-Hermitian matrices, automatically. In the case that the coupled linear matrix equations are consistent, the least-norm Hermitian reflexive and skew-Hermitian solution groups can be computed by choosing suitable initial iterative matrix groups. In addition, the unique optimal approximate Hermitian reflexive and skew-Hermitian solution groups to given arbitrary matrix groups are derived. Finally, some numerical experiments are reported to illustrate the validity of our established theoretical results and feasibly of the presented algorithm.
A new iterative algorithm is suggested for calculating spectral parameters of a quadratic bunch of partially symmetrical compact operators in the Hilbert space.
A new iterative algorithm is suggested for calculating spectral parameters of a quadratic bunch of partially symmetrical compact operators in the Hilbert space.
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