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Analysis of least squares finite element methods for a parameter-dependent first-order system
(1998-01-01)
Yang, SY
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
A parameter-dependent first-order system arising from elasticity problems is introduced. The system corresponds to the 2D isotropic elasticity equations under a stress-pressure-displacement formulation in which the nonnegative parameter measures the material compressibility for the elastic body. Standard and weighted least squares finite element methods are applied to this system, and analyses for different values of the parameter are performed in a unified manner. The methods offer certain advantages such as they need not satisfy the Babuska-Brezzi condition, a single continuous piecewise polynomial space can be used for the approximation of all the unknowns, the resulting algebraic system is symmetric and positive definite, accurate approximations of all the unknowns can be obtained simultaneously, and, especially, computational results do not exhibit any significant numerical locking as the parameter tends to zero which corresponds to the incompressible elasticity problem (or equivalently, the Stokes problem). With suitable boundary conditions, it is shown that both methods achieve optimal rates of convergence in the H-1-norm and in the L-2-norm for all the unknowns. Numerical experiments with various values of the parameter are given to demonstrate the theoretical estimates.
Least-squares finite element methods for the elasticity problem
(1997-12-18)
Yang, SY
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
A new first-order system formulation for the linear elasticity problem in displacement-stress form is proposed. The formulation is derived by introducing additional variables of derivatives of the displacements, whose combinations represent the usual stresses. Standard and weighted least-squares finite element methods are then applied to this extended system. These methods offer certain advantages such as that they need not satisfy the inf-sup condition which is required in the mixed finite element formulation, that a single continuous piecewise polynomial space can be used for the approximation of all the unknowns, that the resulting algebraic systems are symmetric and positive definite, and that accurate approximations of the displacements and the stresses can be obtained simultaneously. With displacement boundary conditions, it is shown that both methods achieve optimal rates of convergence in the H-1-norm and in the L-2-norm for all the unknowns. Numerical experiments with various Poisson ratios are given to demonstrate the theoretical error estimates.
In-domain neighborhood approach to heterogeneous dynamic load balancing in real world network
(2013-01-01)
Daraghmi, Eman Yasser
;
Yuan, Shyan Ming
;
資訊工程學系
;
Department of Computer Science
In this paper, we present a novel in-domain neighborhood approach to clarify the dynamic load balancing problem on a heterogeneous network and to solve many practical problems. The distributed system consists of a network of workstations with different domains, speeds and capacities. Since the number of workstations and the diameter of the network affect the convergences rate, our approach introduces the in-domain relation that classifies the entire network into sub-networks called domains. The algorithm runs in each workstation in order to reach the fairness state in-domain and in entire network rapidly. In this paper, our approach is applied to a cafeteria system as a case study, each workstation is viewed as a cafeteria where the maximum number of orders that can be submitted to one cafeteria corresponds to the capacity of that cafeteria workstation, the communication channels are modeled between the in-domain cafeterias, and the workload is represented as orders. An algorithm is presented to simulate the migration of the orders between in-domain cafeterias and to distribute a proportion of the excessive workload of heavily loaded node to lightly loaded node by considering the capacity of each node such that when the algorithm terminates, the effective-load in all cafeterias is the same. Therefore, each workstation receives an amount of workload proportional to its total capacity. This framework is analyzed mathematically, and it is proved that the proposed algorithm converges and achieves the fairness state.
數位新聞學與數位新聞產業發展關聯性研究：舊媒體、新媒體、新新媒體之聚合效應如何影響當代新聞、市場與民主
(2011)
林照真
;
Lin Chao Chen
;
國立交通大學傳播與科技學系
數位時代結合傳統媒體、以及不同時間崛起的各式新興媒體，已經形成前所未見的媒體新紀元。新興媒體的崛起、互動式的積極運作模式、以及新舊媒體結合而成的新聞運作模式，已經構築出截然不同於傳統新聞產製與消費的「數位新聞學」。數位新聞學不但形成新聞內容生產者與閱聽眾完全不同的互動關係；不同新興媒體介入新聞的經營，也因內含互動與免費等多項利多因素，開始發展型態互有差異的數位新聞產業。除了新興媒體挾帶新聞內容、成為愈來愈重要的社群網絡外，就連傳統媒體也開始多角化經營各式新興媒體，形成台灣媒體市場前所未見的新聞競爭現象。但也因此引發另一重要的問題是，由於台灣數位新聞內容與數位新聞產業的發展，更令人關注有關審議民主與溝通理性等價值，是否可能因為數位新聞學的出現而得以實現。本計畫主旨在於從新聞學角度，探討新舊媒體如何操作與發展新聞產業。本計畫將就台灣之舊媒體（報紙、廣播、電視）、新媒體（谷歌網站、奇摩網等入口網站、一般網站）、新新媒體（部落格、撲浪或推特、臉書、YouTube、手機、網路遊戲）等各式新舊媒體如何產製新聞，以及新聞產業的聚合策略提出事實觀察，並進行廣告市場競爭、新聞價值探索、與新聞倫理的檢討與反思。本計畫預計探討的重點議題為以下六項：一、新媒體、新興媒體介入新聞產業中，是提升、還是降低了新聞水準；二、新媒體科技的崛起，對社會大眾是否產生一定的助益；三、新舊媒體的交互運用與聚合效應，如何競逐廣告市場；對傳統新聞產製、新聞組織產生何種影響；四、新舊媒體如何經營新聞內容，對審議民主與溝通理性等社會價值有何影響；五、傳統新聞記者與公民記者、素人記者在新舊媒體中的角色與定位；六、新興媒體介入新聞運作、以及新舊媒體交融產生新的新聞媒體產業後，如何形成新聞產業自律，並針對其所形成的新聞倫理問題與探討。
A unified analysis of a weighted least squares method for first-order systems
(1998-06-01)
Yang, SY
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
A unified analysis of a weighted least squares finite element method (WLSFEM) for approximating solutions of a large class of first-order differential systems is proposed. The method exhibits several advantageous features. For example, the trial and test functions are not required to satisfy the boundary conditions. Its discretization results in symmetric and positive definite algebraic systems with condition number O(h(-2) + w(2)). And a single piecewise polynomial finite element space may be used for all test and trial functions. Asymptotic convergence of the least squares approximations with suitable weights is established in a natural norm without requiring extra smoothness of the solutions. If instead, the solutions are sufficiently regular, a priori error estimates can be derived under two suitable assumptions which are related respectively to the symmetric positive systems of Friedrichs and first-order Agmon-Douglis-Nirenberg (ADN) elliptic systems. Numerous model problems fit into these two important systems. Some selective examples are examined and verified in the unified framework. (C) 1998 Published by Elsevier Science Inc. All rights reserved.
On the convergence and stability of the standard least squares finite element method for first-order elliptic systems
(1998-07-01)
Yang, SY
;
應用數學系
;
Department of Applied Mathematics
A general framework of the theoretical analysis for the convergence and stability of the standard least squares finite element approximations to boundary value problems of first-order linear elliptic systems is established in a natural norm. With a suitable density assumption, the standard least squares method is proved to be convergent without requiring extra smoothness of the exact solutions. The method is also shown to be stable with respect to the natural norm. Some representative problems such as the grad-div type problems and the Stokes problem are demonstrated. (C) 1998 Published by Elsevier Science Inc. All rights reserved.
On the properties of the reduction-by-composition LMS algorithm
(1999-11-01)
Chen, SG
;
Kao, YA
;
Chen, CY
;
電子工程學系及電子研究所
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Department of Electronics Engineering and Institute of Electronics
The recently proposed low-complexity reduction-by-composition least-mean-square (LMS) algorithm (RCLMS) costs only half multiplications compared to that of the conventional direct-form LMS algorithm (DLMS), This work intends to characterize its properties and conditions for mean and mean-square convergence. Closed-form mean-square error (MSE) as a function of the LMS step-size mu and an extra compensation step-size alpha are derived, which are slightly larger than that of the DLMS algorithm. It is shown, when mu is small enough and alpha is properly chosen, the RCLMS algorithm has comparable performance to that of the DLMS algorithm. Simple working rules and ranges for alpha and mu to make such comparability are provided. For the algorithm to converge, a tight hound for alpha is also derived. The derived properties and conditions are verified by simulations.
A vector neural network for emitter identification
(2002-08-01)
Shieh, CS
;
Lin, CT
;
電控工程研究所
;
Institute of Electrical and Control Engineering
This paper proposes a three-layer vector neural network (VNN) with a supervised learning algorithm suitable for signal classification in general, and for emitter identification (EID) in particular. The VNN can accept interval-value input data as well as scalar input data. The input features of the EID problems include the radio frequency, pulse width, and pulse repetition interval of a received emitter signal. Since the values of these features vary in interval ranges in accordance with a specific radar emitter, the VNN is proposed to process interval-value data in the EID problem. In the training phase, the interval values of the three features are presented to the input nodes of VNN. A new vector-type backpropagation learning algorithm is derived from an error function defined by the VNN's actual output and the desired output indicating the correct emitter type of the corresponding feature intervals. The algorithm can tune the weights of VNN optimally to approximate the nonlinear mapping between a given training set of feature intervals and the corresponding set of desired emitter types. After training, the VNN can be used to identify the sensed scalar-value features from a real-time received emitter signal. A number of simulations are presented to demonstrate the effectiveness and identification capability of VNN, including the two-EID problem and the multi-EID problem with/without additive noise. The simulated results show that the proposed algorithm cannot only accelerate the convergence speed, but it can help avoid getting stuck in bad local minima and achieve higher classification rate.
Spectral analysis of some iterations in the Chandrasekhar's H-functions
(2003-08-01)
Juang, J
;
Lin, KY
;
Lin, WW
;
應用數學系
;
Department of Applied Mathematics
Two very general, fast and simple iterative methods were proposed by Bosma and de Rooij (Bosma, P. B., de Rooij, W. A. (1983). Efficient methods to calculate Chandrasekhar's H functions. Astron. Astrophys. 126:283--292.) to determine Chandrasekhar's H-functions. The methods are based on the use of the equation 'j h = (F) over tilde (h), where (F) over tilde = ((f1) over tilde, (f2) over tilde, . . . (f(n)) over tilde")(T) is a nonlinear map from R-n to R-n. Here (f(i)) over tilde = 1 /(root1 - c + Sigma(k=1)(n) (c(k)mu(k)h(k)/mu(i) + mu(k)), 0 < c less than or equal to 1, i = 1,2, . . . ,n. One such method is essentially a nonlinear Gauss-Seidel iteration with respect to (F) over tilde. The other ingenious approach is to normalize each iterate after a nonlinear Gauss-Jacobi iteration with respect to (F) over tilde is taken. The purpose of this article is two-fold. First, we prove that both methods converge locally. Moreover, the convergence rate of the second iterative method is shown to be strictly less than (root3 - 1)/2. Second, we show that both the Gauss-Jacobi method and Gauss-Seidel method with respect to some other known alternative forms of the Chandrasekhar's H-functions either do not converge or essentially stall for c = 1.
Multistability and convergence in delayed neural networks
(2007-01-01)
Cheng, Chang-Yuan
;
Lin, Kuang-Hui
;
Shih, Chih-Wen
;
應用數學系
;
Department of Applied Mathematics
We present the existence of 2(n) stable stationary solutions for a general n-dimensional delayed neural networks with several classes of activation functions. The theory is obtained through formulating parameter conditions motivated by a geometrical observation. Positively invariant regions for the flows generated by the system and basins of attraction for these stationary solutions are established. The theory is also extended to the existence of 2(n) limit cycles for the n-dimensional delayed neural networks with time-periodic inputs. It is further confirmed that quasiconvergence is generic for the networks through justifying the strongly order preserving property as the self-feedback time lags are small for the neurons with negative self-connection weights. Our theory on existence of multiple equilibria is then incorporated into this quasiconvergence for the network. Four numerical simulations are presented to illustrate our theory. (c) 2006 Elsevier B.V. All rights reserved.

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