On linear stability of predictor–corrector algorithms for fractional differential equations

This paper deals with the numerical approximation of differential equations of fractional order by means of predictor–corrector algorithms. A linear stability analysis is performed and the stability regions of different methods are compared. Furthermore the effects on stability of multiple corrector iterations are verified.     

Multisite co-allocation scheduling algorithms for parallel jobs in computing grid environments

Cooperation of multi-domain massively parallel processor systems in com- puting grid environment provides new opportunities for multisite job scheduling. At the same time, in the area of co-allocation, heterogeneity, network adaptability and scalability raise the challenge for the international design of multisite job scheduling models and algorithms. It presents multisite job scheduling schema through the introduction of mul- tisite job scheduling model and the performance model under the grid environment. It introduces two job multisite and cooperative scheduling models and algorithms with the core of the optimal and greedy-heuristic resource selection strategies. Meanwhile, com- pared with single and multisite cooperative scheduling models and algorithms introduced by Sabin, Yahyapour and other persons, the validity and advance of the scheduling model and the performance model herein are proved.     

On the abs algorithms for perturbed linear systems ∗

One of the most important problems in numerical analysis and numerical optimization is to solve a linear system of equations. Sometimes it should be repeated when one of the equations is replaced by a new one. In this paper as a result of theoretical analysis, an algorithm model and a particular algorithm which are based on the ABS class are proposed. After the original linear system has been solved by the ABS class, the algorithms proposed here can efficiently solve the new system which is obtained from the original system by replacing one of its equations by using information obtained in the previous computation. These algorithms can be used continually when some equations of the original system are replaced by new equations successively with less computation effort.     

Spectral–spatial co-clustering of hyperspectral image data based on bipartite graph

The high dimensionality of hyperspectral images are usually coupled with limited data available, which degenerates the performances of clustering techniques based only on pixel spectral. To improve the performances of clustering, incorporation of spectral and spatial is needed. As an attempt in this direction, in this paper, we propose an unsupervised co-clustering framework to address both the pixel spectral and spatial constraints, in which the relationship among pixels is formulated using an undirected bipartite graph. The optimal partitions are obtained by spectral clustering on the bipartite graph. Experiments on four hyperspectral data sets are performed to evaluate the effectiveness of the proposed framework. Results also show our method achieves similar or better performance when compared to the other clustering methods.     

Least squares based iterative algorithms for identifying Box–Jenkins models with finite measurement data

A least squares based iterative identification algorithm is developed for Box–Jenkins models (or systems). The proposed iterative algorithm can produce highly accurate parameter estimation compared with recursive approaches. The basic idea of the proposed iterative method is to adopt the interactive estimation theory: the parameter estimates relying on unknown variables are computed by using the estimates of these unknown variables which are obtained from the preceding parameter estimates. The numerical example indicates that the proposed iterative algorithm has fast convergence rates compared with the gradient based iterative algorithm.     

Decomposition based hybrid VNS–TS algorithm for distributed parallel factories scheduling with virtual corporation

The main purpose of this paper is to develop a decomposition based hybrid variable neighborhood search/tabu search (DVT) algorithm for multi-factory production network scheduling problem where a number of different individual factories collaborate despite their different objectives. It is assumed some of the network's factories are interested in total processing cost minimization whereas the remaining factories are interested in the production profits maximization. It is also assumed that jobs can migrate from their original factory to other factories but a transportation time is incurred. Our proposed algorithm comprises of a tabu search and a variable neighborhood search with several local search algorithms. In this hybridization, to improve the search ability of the algorithm, we make use of guiding principles with ordering of neighborhood structures by mixed integer linear programming relaxation. In the proposed algorithm, the parallel search strategy is designed for a scalar bi-objective. Multiple objectives are combined with L₁-metric technique then each sub-search procedure evolves separately until a good approximation of the Pareto-front is obtained. The non-dominated sets obtained from our algorithm and original heuristic (algorithm without ordering concept) are compared using three different indices. Furthermore, the problem is modeled as a mixed integer linear programming and solved by improved ϵ-constraint approach (IEA) with CPLEX solver. The results of comparisons between IEA and DVT algorithm showed the proposed algorithm yielded most of the solutions in the net non-dominated front.     

On the space–time of optimal, approximate and streaming algorithms for synopsis construction problems

Synopses construction algorithms have been found to be of interest in query optimization, approximate query answering and mining, and over the last few years several good synopsis construction algorithms have been proposed. These algorithms have mostly focused on the running time of the synopsis construction vis-a-vis the synopsis quality. However the space complexity of synopsis construction algorithms has not been investigated as thoroughly. Many of the optimum synopsis construction algorithms are expensive in space. For some of these algorithms the space required to construct the synopsis is significantly larger than the space required to store the input. These algorithms rely on the fact that they require a smaller “working space” and most of the data can be resident on disc. The large space complexity of synopsis construction algorithms is a handicap in several scenarios. In the case of streaming algorithms, space is a fundamental constraint. In case of offline optimal or approximate algorithms, a better space complexity often makes these algorithms much more attractive by allowing them to run in main memory and not use disc, or alternately allows us to scale to significantly larger problems without running out of space. In this paper, we propose a simple and general technique that reduces space complexity of synopsis construction algorithms. As a consequence we show that the notion of “working space” proposed in these contexts is redundant. This technique can be easily applied to many existing algorithms for synopsis construction problems. We demonstrate the performance benefits of our proposal through experiments on real-life and synthetic data. We believe that our algorithm also generalizes to a broader range of dynamic programs beyond synopsis construction. Sudipto Guha’s research supported in part by an Alfred P. Sloan Research Fellowship and by NSF Awards CCF-0430376, CCF-0644119.A preliminary version of the paper appeared as “Space efficiency in synopsis construction algorithms”, VLDB Conference 2005, Trondheim, [19].     

Computational performance of basic state reduction based dynamic programming algorithms for bi-objective 0–1 knapsack problems

This paper studies a group of basic state reduction based dynamic programming (DP) algorithms for the multi-objective 0–1 knapsack problem (MKP), which are related to the backward reduced-state DP space (BRDS) and forward reduced-state DP space (FRDS). The BRDS is widely ignored in the literature because it imposes disadvantage for the single objective knapsack problem (KP) in terms of memory requirements. The FRDS based DP algorithm in a general sense is related to state dominance checking, which can be time consuming for the MKP while it can be done efficiently for the KP. Consequently, no algorithm purely based on the FRDS with state dominance checking has ever been developed for the MKP. In this paper, we attempt to get some insights into the state reduction techniques efficient to the MKP. We first propose an FRDS based algorithm with a local state dominance checking for the MKP. Then we evaluate the relative advantage of the BRDS and FRDS based algorithms by analyzing their computational time and memory requirements for the MKP. Finally different combinations of the BRDS and FRDS based algorithms are developed on this basis. Numerical experiments based on the bi-objective KP instances are conducted to compare systematically between these algorithms and the recently developed BRDS based DP algorithm as well as the existing FRDS based DP algorithm without state dominance checking.     

RK–Butcher algorithms for singular system-based electronic circuit

In this paper, a new method of analysis for a singular system-based electronic circuits using the Runge–Kutta (RK)–Butcher algorithm is presented for linear time-invariant and time-varying cases. The discrete solutions obtained using the RK–Butcher algorithms are compared with the exact solutions of the electronic circuit problem and are found to be very accurate. Stability regions for the Single term walsh series method and the RK–Butcher algorithms are presented. Error graphs for inductor currents and capacitor voltages are presented in a graphical form to show the efficiency of this method. This RK–Butcher algorithm can be easily implemented in a digital computer and the solution can be obtained for any length of time.     

Partitioned strong coupling algorithms for fluid–structure interaction

Numerical simulation of fluid–structure interaction is often attempted in the context of partitioned methods, where already existing solvers for fluid or structure alone are used jointly. Mostly this is done by exchanging information from time step to time step in an alternating fashion. These weak coupling methods are explicit and hence suffer from possible instabilities. Therefore often strong coupling––where equilibrium is satisfied jointly between fluid and structure in each time step––is desired; the simplest computational procedure is similar to the time stepping an alternating iteration. We show why also this approach may experience difficulties, and how they may be circumvented with block-Newton methods, still in the partitioned framework, by only using the solvers of the subproblems fluid and structure.     

Real-time 2D–3D filtering using order statistics based algorithms

The paper presents a review of the author’s own results obtained in the last several years. Some examples of real-time processing of 2D and 3D images are described. In particular, we discuss the noise model and objective criteria that can be applied to characterize the performance of the processing algorithms. Several proposed algorithms based on RM approach are compared with other known ones, demonstrating the advantages in noise suppressing and preservation of fine image details and edges. A number of 2D and 3D image denoising filters are implemented on DSP, realizing real-time mode in the image processing. The performances of the proposed processing algorithms and the known ones are discussed and evaluated here.

An optimal time–space algorithm for dense stereo matching

The increasing demand for higher resolution images and higher frame rate videos will always pose a challenge to computational power when real-time performance is required to solve the stereo-matching problem in 3D reconstruction applications. Therefore, the use of asymptotic analysis is necessary to measure the time and space performance of stereo-matching algorithms regardless of the size of the input and of the computational power available. In this paper, we survey several classic stereo-matching algorithms with regard to time–space complexity. We also report running time experiments for several algorithms that are consistent with our complexity analysis. We present a new dense stereo-matching algorithm based on a greedy heuristic path computation in disparity space. A procedure which improves disparity maps in depth discontinuity regions is introduced. This procedure works as a post-processing step for any technique that solves the dense stereo-matching problem. We prove that our algorithm and post-processing procedure have optimal O(n) time–space complexity, where n is the size of a stereo image. Our algorithm performs only a constant number of computations per pixel since it avoids a brute force search over the disparity range. Hence, our algorithm is faster than “real-time” techniques while producing comparable results when evaluated with ground-truth benchmarks. The correctness of our algorithm is demonstrated with experiments in real and synthetic data.     

A highly parallel Black–Scholes solver based on adaptive sparse grids

In this paper, we present a highly efficient approach for numerically solving the Black–Scholes equation in order to price European and American basket options. Therefore, hardware features of contemporary high performance computer architectures such as non-uniform memory access and hardware-threading are exploited by a hybrid parallelization using MPI and OpenMP which is able to drastically reduce the computing time. In this way, we achieve very good speed-ups and are able to price baskets with up to six underlyings. Our approach is based on a sparse grid discretization with finite elements and makes use of a sophisticated adaption. The resulting linear system is solved by a conjugate gradient method that uses a parallel operator for applying the system matrix implicitly. Since we exploit all levels of the operator's parallelism, we are able to benefit from the compute power of more than 100 cores. Several numerical examples as well as an analysis of the performance for different computer architectures are provided.     

Dynamic visual tracking based on multiple feature matching and g–h filter

The area-based matching approach has been used extensively in many dynamic visual tracking systems to detect moving targets because it is computation efficient and does not require an object model. Unfortunately, area-based matching is sensitive to occlusion and illumination variation. In order to improve the robustness of visual tracking, two image cues, i.e., target template and target contour, are used in the proposed visual tracking algorithm. In particular, the target contour is represented by the active contour model that is used in combination with the fast greedy algorithm. However, to use the conventional active contour method, the initial contour needs to be provided manually. In order to facilitate the use of contour matching, a new approach that combines the adaptive background subtraction method with the border tracing technique was developed and is used to automatically generate the initial contour. In addition, a g–h filter is added to the visual loop to deal with the latency problem of visual feedback so that the performance of dynamic visual tracking can be improved. Experimental results demonstrate the effectiveness of the proposed approach.     

System reliability for non-repairable multi-state series–parallel system using fuzzy Bayesian inference based on prior interval probabilities

In this article, the fuzzy concepts are applied in analysis of the system reliability problem. The fuzzy number is used to construct the fuzzy reliability of the non-repairable multi-state series–parallel system (NMSS). The fuzzy failure rate function is represented by an exponential fuzzy number. By using this innovative approach, the fuzzy system reliability of NMSS is created. In order to analyse this fuzzy system reliability, the fuzzy Bayesian point estimate of fuzzy system reliability is made by the conventional Bayesian formula. And, the posterior fuzzy system reliability of NMSS is developed by Bayesian inference with fuzzy probabilities. Finally, the performance of the method is measured by the mean square error of fuzzy Bayesian point estimate for the fuzzy system reliability of NMSS.     

Dual–primal proximal point algorithms for extended convex programming

This paper presents a class of dual–primal proximal point algorithms (PPAs) for extended convex programming with linear constraints. By choosing appropriate proximal regularization matrices, the application of the general PPA to the equivalent variational inequality of the extended convex programming with linear constraints can result in easy proximal subproblems. In theory, the sequence generated by the general PPA may fail to converge since the proximal regularization matrix is asymmetric sometimes. So we construct descent directions derived from the solution obtained by the general PPA. Different step lengths and descent directions are chosen with the negligible additional computational load. The global convergence of the new algorithms is proved easily based on the fact that the sequences generated are Fejér monotone. Furthermore, we provide a simple proof for the O(1/t) convergence rate of these algorithms.     

Distributed leaderless consensus algorithms for networked Euler–Lagrange systems

This article proposes and analyses distributed, leaderless, model-independent consensus algorithms for networked Euler–Lagrange systems. We propose a fundamental consensus algorithm, a consensus algorithm accounting for actuator saturation, and a consensus algorithm accounting for unavailability of measurements of generalised coordinate derivatives, for systems modelled by Euler–Lagrange equations. Due to the fact that the closed-loop interconnected Euler–Lagrange equations using these algorithms are non-autonomous, Matrosov's theorem is used for convergence analysis. It is shown that consensus is reached on the generalised coordinates and their derivatives of the networked Euler–Lagrange systems as long as the undirected communication topology is connected. Simulation results show the effectiveness of the proposed algorithms.     

Hybrid algorithms for the twin–screw extrusion configuration problem

The twin-screw configuration problem (TSCP) arises in the context of polymer processing, where twin-screw extruders are used to prepare polymer blends, compounds or composites. The goal of the TSCP is to define the configuration of a screw from a given set of screw elements. The TSCP can be seen as a sequencing problem as the order of the screw elements on the screw axis has to be defined. It is also inherently a multi-objective problem since processing has to optimize various conflicting parameters related to the degree of mixing, shear rate, or mechanical energy input among others. In this article, we develop hybrid algorithms to tackle the bi-objective TSCP. The hybrid algorithms combine different local search procedures, including Pareto local search and two phase local search algorithms, with two different population-based algorithms, namely a multi-objective evolutionary algorithm and a multi-objective ant colony optimization algorithm. The experimental evaluation of these approaches shows that the best hybrid designs, combining Pareto local search with a multi-objective ant colony optimization approach, outperform the best algorithms that have been previously proposed for the TSCP.     

Automatic generation of fast algorithms for matrix–vector multiplication

This paper describes the methods for finding fast algorithms for computing matrix–vector products including the procedures based on the block-structured matrices. The proposed methods involve an analysis of the structural properties of matrices. The presented approaches are based on the well-known optimization techniques: the simulated annealing and the hill-climbing algorithm along with its several extensions. The main idea of the proposed methods consists in finding a decomposition of the original matrix into a sparse matrix and a matrix corresponding to an appropriate block-structured pattern. The main criterion for optimizing is a reduction of the computational cost. The methods presented in this paper can be successfully implemented in many digital signal processing tasks.