Iterative Algorithm

A numerical algorithm for computing necessary conditions for performance specifications is developed for nonlinear uncertain systems. The algorithm is similar in nature and behavior to the power algorithm for the p lower bound, and doesn't rely on a descent method. The algorithm is applied to a practical example.

The Algebraic Reconstruction Technique (ART) is an iterative image reconstruction algorithm. During the development of the Clear-PEM device, a PET scanner designed for the evaluation of breast cancer, multiple tests were done in order to optimise the reconstruction process. The comparison between ART, MLEM and OSEM indicates that ART can perform faster and with better image quality than the other, most common algorithms. It is claimed in this paper that if ART's relaxation parameter is carefully adjusted to the reconstruction procedure it can produce high quality images in short computational time. This is confirmed by showing that with the relaxation parameter evolving as a logarithmic function, ART can match in terms of image quality and overcome in terms of computational time the performance of MLEM and OSEM algorithms. However, this study was performed only with simulated data and the level of noise with real data may be different.

The main goal of this paper is to present a numerical model describing the major physical phenomena involved in electromagnetic casting industrial processes as precisely as possible. Under suitable physical assumptions, we derive the set of equations in the two-dimensional case; we describe in detail the numerical methods used to solve such equations and derive an iterative algorithm. Numerical results describing the case of an aluminium ingot are presented in order to show the efliciency of the method. lc'

For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter. A simple algorithm for approximating a minimum k-way cut

This work investigates dynamics of a two-stage gear system involving backlash and timedependent mesh stiffness. This paper mainly consists to develop a 12 degree of freedom gear dynamic model. The model consists of a two-stage spur gear, three shafts, and two inertias representing load and prime mover and three bearings. Gear contact is characterised by a periodically changing stiffness and a backlash which can lead to loss of the contact. The nonlinear dynamic response of the system is studied thanks to a technique of linearization which decomposes the nonlinear system into some linear systems satisfying some conditions. Each system is solved thanks to the Newmark iterative algorithm. The results obtained appear to be the phenomenon of loss of teeth contact because of the discontinuity of the kinematic movement between the motives and receiving components of the system.

The Radon transform (RT) suffers from the typical problems of loss of resolution and aliasing that arise as a consequence of incomplete information, including limited aperture and discretization. Sparseness in the Radon domain is a valid and useful criterion for supplying this missing information, equivalent somehow to assuming smooth amplitude variation in the transition between known and unknown (missing) data. Applying this constraint while honoring the data can become a serious challenge for routine seismic processing because of the very limited processing time available, in general, per common midpoint. To develop methods that are robust, easy to use and flexible to adapt to different problems we have to pay attention to a variety of algorithms, operator design, and estimation of the hyperparame-ters that are responsible for the regularization of the solution. In this paper, we discuss fast implementations for several varieties of RT in the time and frequency domains. An iterative conjugate gradient algorithm with fast Fourier transform multiplication is used in all cases. To preserve the important property of iterative subspace methods of regularizing the solution by the number of iterations, the model weights are incorporated into the operators. This turns out to be of particular importance, and it can be understood in terms of the singular vectors of the weighted transform. The iterative algorithm is stopped according to a general cross validation criterion for subspaces. We apply this idea to several known implementations and compare results in order to better understand differences between, and merits of, these algorithms.

For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter. A simple algorithm for approximating a minimum k-way cut

The present paper describes a mathematical model for evaluating cooling potential of green roof and solar thermal shading in buildings. A control volume approach based on finite difference methods is used to analyze the components of green roof, viz. green canopy, soil and support layer. Further, these individual decoupled models are integrated using Newton's iterative algorithm until the convergence for continuity of interface state variables is achieved. The green roof model is incorporated in the building simulation code using fast Fourier transform (FFT) techniques in Matlab. The model is validated against the experimental data from a similar green roof-top garden in Yamuna Nagar (India), and is then used to predict variations in canopy air temperature, entering heat flux through roof and indoor air temperature. The model is found to be very accurate in predicting green canopy-air temperature and indoor-air temperature variations (error range 73.3%, 76.1%, respectively). These results are further used to study thermal performance of green roof combined with solar shading. Cooling potential of green roof is found adequate (3.02 kWh per day for LAI of 4.5) to maintain an average room air temperature of 25.7 1C. The present model can be easily coupled to different greenhouse and building simulation codes. r

Purpose -The purpose of this paper is to propose a robust method to estimate the parameters of Jiles-Atherton model of ferromagnetic hysteresis by fitting the model to symmetrical hysteresis loops. The performance of the method is evaluated by both theoretical and experimental data. Design/methodology/approach -Jiles-Atherton model with five parameters describes the hysteretic behaviour of ferromagnetic materials. To calculate the model parameters, the most common data displaying the hysteresis features are the hysteresis loops stimulated by symmetrical steady state excitations, e.g. sinusoidal sources. Using the characteristic equations at specific points on these hysteresis loops, the Jiles-Atherton model parameters can be determined by curve fitting and numerical optimized iteration. Findings -Practicality and robustness were not well considered by the conventional parameter estimation method: the initial curve starting from demagnetization is not always available and a direct iterative algorithm to solve the characteristic equations is sensitive to the initial values of the iteration and the evaluation order of the equations because of two main reasons. The first one is that the basic equation group has non-unique solutions, which is caused by the nonlinearity of the characteristic equations and the fact that there are more unknown quantities (i.e. five model parameters) than the equations available; the second reason is the multimodal feature of the problem, which means that there are many local minima for the iteration algorithm to be trapped in. So curve fitting around the loop tips is proposed before numerical iteration. The goal is to make the initial values, particularly saturation magnetization M s , not far away from the desired solution to increase the possibility of converging to a physical result. The optimized iterative method with the enhanced ability to avoid local minima and find global roots is then applied to obtain the model parameters.

Friction in hydraulic actuators can be described using nonlinear, velocity dependent models. In this paper, the friction is described by an exponential Stribeck friction model. An iterative algorithm is presented to identify the friction model parameters. The method fits two lines on the experimental data relating steady-state velocities to actuator pressure differentials. The parameters of the fitted lines are obtained using an iterative optimization technique. Based on the obtained parameters, the original nonlinear friction model parameters are completely reconstructed. The proposed method is validated by building a simulation model for a valve-controlled hydraulic system in which the friction is modeled based on the method described here. The proposed method can be used in practical situations, whereby fast and reliable identification of major parameters of the friction in hydraulic actuators is needed with easy to obtained pressure measurements.

This paper presents a new multiplier with possibility to achieve an arbitrary accuracy. The multiplier is based upon the same idea of numbers representation as Mitchell's algorithm, but does not use logarithm approximation. The proposed iterative algorithm is simple and efficient, achieving an error percentage as small as required, until the exact result. Hardware solution involves adders and shifters, so it is not gate and power consuming. Parallel circuits are used for error correction. The error summary for operands ranging from 8-bits to 16-bits operands indicates very low error percentage with only two parallel correction circuits.

In this paper, we consider a linear mixed model with measurement errors in fixed effects. We find the corrected score function estimators for the variance components. An iterative algorithm is proposed for estimating the parameters. The computations on each iteration of this algorithm are those associated with computing estimates of fixed and random effects for given values of the variance components. We also derive the consistency of the estimators under regularity conditions. The simulation study shows that for relatively small sample size the corrected estimators perform very well. Finally, an example of real data is given for illustration.

For reconstruction of low-rank matrices from undersampled measurements, we develop an iterative algorithm based on least-squares estimation. While the algorithm can be used for any low-rank matrix, it is also capable of exploiting a-priori knowledge of matrix structure. In particular, we consider linearly structured matrices, such as Hankel and Toeplitz, as well as positive semidefinite matrices. The performance of the algorithm, referred to as alternating least-squares (ALS), is evaluated by simulations and compared to the Cramér-Rao bounds.

This work presents a Multilevel Schwarz Shooting method for the numerical solution of the Poisson equation, using a five point finite difference molecule, and subject to Dirichlet boundary conditions, which arises in two dimensional incompressible flow simulations. The iterative simple shooting algorithm utilized has optimal complexity, but becomes unstable when the problem size is increased. In this work, this limitations is overcome using a domain decomposition technique, more specifically, the alternating Schwarz method, which is used to generalize the iterative multiple shooting approach in the partial differential equation (PDE) context. In order to accelerate the convergence of the algorithm a multilevel approach is used. The resulting iterative algorithm has optimal complexity and is scalable in terms of problem size. Results of computational experiments are presented for the Poisson equation and for the two dimensional incompressible Navier-Stokes equation using the stream function-vorticity formulation.

We propose an iterative algorithm to generate a sequence of a prescribed number of points on a parametric curve with control of their distribution. Our algorithm depends on a free parameter which controls the achievement of a final distribution of points lying between two extreme cases: uniform arc length distribution and bending energy dependent distribution. This is obtained by computing a reparametrization function that interpolates the inverse of the arc length function at equidistant arguments. The proposed reparametrization function is a C 1 rational linear spline, therefore if the original curve is a NURBS then the reparametrized curve is also a NURBS of the same degree, but with an enlarged set of knots.

In this paper, the optimal strategies for discrete-time linear system quadratic zero-sum games related to the H-infinity optimal control problem are solved in forward time without knowing the system dynamical matrices. The idea is to solve for an action dependent value function Q(x, u, w) of the zero-sum game instead of solving for the state dependent value function V (x) which satisfies a corresponding game algebraic Riccati equation (GARE). Since the state and actions spaces are continuous, two action networks and one critic network are used that are adaptively tuned in forward time using adaptive critic methods. The result is a Q-learning approximate dynamic programming (ADP) modelfree approach that solves the zero-sum game forward in time. It is shown that the critic converges to the game value function and the action networks converge to the Nash equilibrium of the game. Proofs of convergence of the algorithm are shown. It is proven that the algorithm ends up to be a model-free iterative algorithm to solve the GARE of the linear quadratic discrete-time zero-sum game. The effectiveness of this method is shown by performing an H-infinity control autopilot design for an F-16 aircraft. ᭧

We present an iterative algorithm (BIN) for scaling all the rows and columns of a real symmetric matrix to unit 2-norm. We study the theoretical convergence properties and its relation to optimal conditioning. Numerical experiments show that BIN requires 2-4 matrix-vector multiplications to obtain an adequate scaling, and in many cases significantly reduces the condition number, more than other scaling algorithms. We present generalizations to complex, nonsymmetric and rectangular matrices.

There was a lot of interest in multicast communications within this decade as it is an essential part of many network applications, e.g. video-on-demand, etc. In this paper, we model flow rate allocation for application overlay as a utility based optimization problem constrained by capacity limitations of physical links and overlay constraints. The optimization flow control presented here addresses not only concave utility functions which are suitable for applications with elastic traffics, but also especial forms of non-concave utilities that are used to model applications with inelastic traffics, which might demand for hard delay and rate requirements. We then propose an iterative algorithm as the solution to the optimization flow control problem and investigate especial forms of non-concave utilities that are supported by this model. Simulation results show that the iterative algorithm can be used to deal with sigmoidal-like utilities which are useful for modeling real-time applications such as live streaming.

This paper is concerned with a compact finite difference method for solving systems of two-dimensional reaction–diffusion equations. This method has the accuracy of fourth-order in both space and time. The existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear term. Three monotone iterative algorithms

We obtain the (Shannon) optimal power and rate allocation strategies for the uplink on single cell systems. For an N user system, we show that successive decoding which is independent of channel state is optimal in the Shannon sense. Using this result, we,frame a simple N dimensional convex optimization problem, which is solved to obtain optimum power and rate allocation as explicit functions of the channel state.

We analyze the long-run availability of a two-unit parallel system sustained by a cold standby unit and attended by two identical repairmen. The system satisfies the usual conditions (i.i.d. random variables, perfect repair, instantaneous and perfect switch, queueing). Each operative unit has a constant failure rate and a general repair time distribution. We use Hokstad's supplementary variable method to construct a system of simultaneous partial differential equations. We present a first-order numerical scheme and an iterative algorithm for the solution of the equations. A particular but important numerical example (Weibull repair), illustrated by computer-plotted graphs, motivates the proposed approximation.

In the present study, we introduce a simple iterative procedure that allows to correct the outputs of a classifier with respect to the new a priori probabilities of a new data set to be scored, even when these new a priori probabilities are unknown in advance. We also show that a significant increase in classification accuracy can be observed when using this procedure properly. More specifically, by applying the correcting procedure on the outputs of a simple logistic regression model, we observed an increase of 5.8% of classification rate on a difficult real-world multi-class problem-the automatic labeling of geographical maps based on remote sensing information. Moreover, the resulting classifier-the logistic regression model whose outputs have been adjusted according to our procedure-outperformed by more that 4% all of our previous models in terms of classification accuracy, including Bagfs (a multiple classifier system based on C4.5 decision trees), the best obtained model up-to-now.

We introduce a new Kern's type inequality and show its usefulness in making the convergence of iterative algorithms for thin elastic structures independent of their thickness. Uno nouvelle i"egalitc de Kom pour de» structures Clasliqlles minces Resume. Nous introduisons une nouvelle inegalite de type Korn, et nous montrons son utilire pour rendre independante de l 'epaisseur la convergence d'algorithmes iteratlfs, dans le cas de structures elastiques minces. Version Irencelse abregce

Motion blur is one of the most common causes of image degradation. It is of increasing interest due to the deep penetration of digital cameras into consumer applications. In this paper, we start with a hypothesis that there is sufficient information within a blurred image and approach the deblurring problem as an optimisation process where the deblurring is to be done by satisfying a set of conditions. These conditions are derived from first principles underlying the degradation process assuming noise-free environments. We propose a novel but effective method for removing motion blur from a single blurred image via an iterative algorithm. The strength of this method is that it enables deblurring without resorting to estimation of the blur kernel or blur depth. The proposed iterative method has been tested on several images with different degrees of blur. The obtained results have been compared with state of the art techniques including those that require more than one input image. The results are consistently of high quality and comparable or superior to the existing methods which demonstrates the effectiveness of the proposed technique.

A stabilized finite element method (FEM) for the multidimensional steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the finite calculus (FIC) method. For 1D problems the stabilization terms act as a nonlinear additional diffusion governed by a single stabilization parameter. It is shown that for multidimensional problems an orthotropic stabilizing diffusion must be added along the principal directions of curvature of the solution. A simple iterative algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described. Numerical results for 1D and 2D problems with sharp gradients are presented showing the effectiveness and accuracy of the new stabilized formulation.

An advanced random phase-shifting algorithm to extract phase distributions from randomly phase-shifted interferograms is proposed. The algorithm is based on a least-squares iterative procedure, but it copes with the limitation of the existing iterative algorithms by separating a frame-to-frame iteration from a pixel-to-pixel iteration. The algorithm provides stable convergence and accurate phase extraction with as few as three interferograms, even when the phase shifts are completely random. The algorithm is simple, fast, and fully automatic. A computer simulation is conducted to prove the concept.

The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Thomann, Isabell (Ph.D., Physics) Generation, Temporal Characterization and Applications of Femtosecond-/ Attosecond Extreme Ultraviolet Pulses Thesis directed by Prof. Margaret M. Murnane

A new frequency-domain (FD) approach is presented for optimal estimation of rational transfer functions coefficients. The proposed method seeks to match any arbitrarily-shaped FD specifications in the least-squares sense. The desired specifications may be arbitrarily spaced in frequency. The design is performed directly in the digital domain, and no analog to digital transformation is necessary. The proposed method makes use of the inherent mathematical structure in this rational modeling problem to theoretically decouple the numerator and denominator estimation problems into two lower dimensional problems. The denominator criterion is nonlinear but possesses a weighted-quadratic structure, which is convenient for iterative optimization. The optimal numerator is found linearly by solving a set of simultaneous equations. The decoupled criteria retain the global optimality properties. The performance of the algorithm is demonstrated with some simulation examples.

This paper considers the problem of scalable distributed coding of correlated sources that are communicated to a central unit. The general setting is typically encountered in sensor networks. The conditions of communication channels between the source encoders and fusion center may be time-varying and it is often desirable to guarantee a base layer of coarse information during channel fades. In addition the desired system should be robust to various scenarios of channel failure and should utilize all the available information to attain the best possible compression efficiency. Although a standard 'Lloyd-style' distributed coder design algorithm can be generalized to scalable distributed source coding, the resulting algorithm depends heavily on initialization and will virtually always converge to a poor local minimum on the distortion-cost surface. We propose an efficient initialization scheme for such a system, which employs a properly designed multi-stage distributed coder. In our prior work, we highlighted the fundamental conflict that arises when multi-stage coding is directly combined with distributed quantization. Here we use the multi-stage distributed coding system to initialize a scalable distributed coder and propose an iterative algorithm for joint design of all system components once the structural constraint is removed. Simulation results show considerable gains over randomly initialized scalable distributed coder design.

In this paper, we apply the Jacobi iterative algorithm to combat intersymbol interference caused by frequency selective channels. An analytical bound of the proposed equalizer is analyzed in order to gain an insight into its asymptotic performance. Due to the error propagation problem, the potential of this algorithm is not reached in an uncoded system. However, its extension to a coded system with the application of the turbo processing principle results in a new turbo equalization algorithm which demonstrates comparable performance with reduced complexity compared to some existing filter based turbo equalization schemes.

The performance of web search engines may often deteriorate due to the diversity and noisy information contained within web pages. User click-through data can be used to introduce more accurate description (metadata) for web pages, and to improve the search performance. However, noise and incompleteness, sparseness, and the volatility of web pages and queries are three major challenges for research work on user click-through log mining. In this paper, we propose a novel iterative reinforced algorithm to utilize the user click-through data to improve search performance. The algorithm fully explores the interrelations between queries and web pages, and effectively finds "virtual queries" for web pages and overcomes the challenges discussed above. Experiment results on a large set of MSN click-through log data show a significant improvement on search performance over the naive query log mining algorithm as well as the baseline search engine.