Search results for: Solution approaches.

Authors: H. Nouri, I. E. Achouri, A. Grimes, H. Ait Said, M. Aissou, Y. Zebboudj

Abstract:

This paper aims to analysis the behavior of DC corona discharge in wire-to-plate electrostatic precipitators (ESP). Currentvoltage curves are particularly analyzed. Experimental results show that discharge current is strongly affected by the applied voltage. The proposed method of current identification is to use the method of least squares. Least squares problems that of into two categories: linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. A closed-form solution (or closed form expression) is any formula that can be evaluated in a finite number of standard operations. The non-linear problem has no closed-form solution and is usually solved by iterative.

Keywords: Electrostatic precipitator, current-voltage characteristics, Least Squares method, electric field, magnetic field.

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Authors: Iftikhar Ahmed Satti, Wan Ismail Wan Yusoff

Abstract:

The structural interpretation of a part of eastern Potwar (Missa Keswal) has been carried out with available seismological, seismic and well data. Seismological data contains both the source parameters and fault plane solution (FPS) parameters and seismic data contains ten seismic lines that were re-interpreted by using well data. Structural interpretation depicts two broad types of fault sets namely, thrust and back thrust faults. These faults together give rise to pop up structures in the study area and also responsible for many structural traps and seismicity. Seismic interpretation includes time and depth contour maps of Chorgali Formation while seismological interpretation includes focal mechanism solution (FMS), depth, frequency, magnitude bar graphs and renewal of Seismotectonic map. The Focal Mechanism Solutions (FMS) that surrounds the study area are correlated with the different geological and structural maps of the area for the determination of the nature of subsurface faults. Results of structural interpretation from both seismic and seismological data show good correlation. It is hoped that the present work will help in better understanding of the variations in the subsurface structure and can be a useful tool for earthquake prediction, planning of oil field and reservoir monitoring.

Keywords: Focal mechanism solution (FMS), Fault plane solution (FPS), Reservoir monitoring, earthquake prediction.

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Authors: S. Zouari, H. Daoud, M. Loulou, P. Loumeau, N. Masmoudi

Abstract:

A wideband 2-1-1 cascaded ΣΔ modulator with a single-bit quantizer in the two first stages and a 4-bit quantizer in the final stage is developed. To reduce sensitivity of digital-to-analog converter (DAC) nonlinearities in the feedback of the last stage, dynamic element matching (DEM) is introduced. This paper presents two modelling approaches: The first is MATLAB description and the second is VHDL-AMS modelling of the proposed architecture and exposes some high-level-simulation results allowing a behavioural study. The detail of both ideal and non-ideal behaviour modelling are presented. Then, the study of the effect of building blocks nonidealities is presented; especially the influences of nonlinearity, finite operational amplifier gain, amplifier slew rate limitation and capacitor mismatch. A VHDL-AMS description presents a good solution to predict system-s performances and can provide sensitivity curves giving the impact of nonidealities on the system performance.

Keywords: behavioural study, DAC nonlinearity, DEM, ΣΔ modulator, VHDL-AMS modelling.

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Authors: Yogi Satrya Aryadinata, Anne Laurent, Michel Sala

Abstract:

Gradual patterns have been studied for many years as they contain precious information. They have been integrated in many expert systems and rule-based systems, for instance to reason on knowledge such as “the greater the number of turns, the greater the number of car crashes”. In many cases, this knowledge has been considered as a rule “the greater the number of turns → the greater the number of car crashes” Historically, works have thus been focused on the representation of such rules, studying how implication could be defined, especially fuzzy implication. These rules were defined by experts who were in charge to describe the systems they were working on in order to turn them to operate automatically. More recently, approaches have been proposed in order to mine databases for automatically discovering such knowledge. Several approaches have been studied, the main scientific topics being: how to determine what is an relevant gradual pattern, and how to discover them as efficiently as possible (in terms of both memory and CPU usage). However, in some cases, end-users are not interested in raw level knowledge, and are rather interested in trends. Moreover, it may be the case that no relevant pattern can be discovered at a low level of granularity (e.g. city), whereas some can be discovered at a higher level (e.g. county). In this paper, we thus extend gradual pattern approaches in order to consider multiple level gradual patterns. For this purpose, we consider two aggregation policies, namely horizontal and vertical.

Keywords: Gradual Pattern.

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Authors: Majid Abdolrazzagh-Nezhad, Salwani Abdullah

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The job-shop scheduling problem (JSSP) is an important decision facing those involved in the fields of industry, economics and management. This problem is a class of combinational optimization problem known as the NP-hard problem. JSSPs deal with a set of machines and a set of jobs with various predetermined routes through the machines, where the objective is to assemble a schedule of jobs that minimizes certain criteria such as makespan, maximum lateness, and total weighted tardiness. Over the past several decades, interest in meta-heuristic approaches to address JSSPs has increased due to the ability of these approaches to generate solutions which are better than those generated from heuristics alone. This article provides the classification, constraints and objective functions imposed on JSSPs that are available in the literature.

Keywords: Job-shop scheduling, classification, constraints, objective functions.

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Authors: M. Ramachandra, G. Dilip Maruthi, R. Rashmi

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This paper aims to study the corrosion property of aluminum matrix nanocomposite of an aluminum alloy (Al-6061) reinforced with zirconium dioxide (ZrO₂) particles. The zirconium dioxide particles are synthesized by solution combustion method. The nanocomposite materials are prepared by mechanical stir casting method, varying the percentage of n-ZrO₂ (2.5%, 5% and 7.5% by weight). The corrosion behavior of base metal (Al-6061) and Al/ZrO₂ nanocomposite in seawater (3.5% NaCl solution) is measured using the potential control method. The corrosion rate is evaluated by Tafel extrapolation technique. The corrosion potential increases with the increase in wt.% of n-ZrO₂ in the nanocomposite which means the decrease in corrosion rate. It is found that on addition of n-ZrO2 particles to the aluminum matrix, the corrosion rate has decreased compared to the base metal.

Keywords: Al6061 alloy, corrosion, solution combustion, stir casting, Potentiostat, Zirconium Dioxide.

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Authors: Daiming Wang

Abstract:

In this paper, a neutral impulsive competition system with distributed delays is studied by using Mawhin-s coincidence degree theory and the mean value theorem of differential calculus. Sufficient conditions on the existence of positive periodic solution of the system are obtained.

Keywords: Neutral impulsive delay system, competitive system, coincidence degree, periodic solution, existence.

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Authors: El Mahdi Barrah, Said Safi, Abdessamad Malaoui

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In this paper, we describe an application for face recognition. Many studies have used local descriptors to characterize a face, the performance of these local descriptors remain low by global descriptors (working on the entire image). The application of local descriptors (cutting image into blocks) must be able to store both the advantages of global and local methods in the Discrete Cosine Transform (DCT) domain. This system uses neural network techniques. The letter method provides a good compromise between the two approaches in terms of simplifying of calculation and classifying performance. Finally, we compare our results with those obtained from other local and global conventional approaches.

Keywords: Face detection, face recognition, discrete cosine transform (DCT), FPLBP, TPLBP, NN.

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Authors: Bubaker M. F. Bushofa, Abdel Hafez A. Azab

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This article is based on the technique which is called Discrete Parameter Tracking (DPT). First introduced by A. A. Azab [8] which is applicable for less order reference model. The order of the reference model is (n-l) and n is the number of the adjustable parameters in the physical plant. The technique utilizes a modified gradient method [9] where the knowledge of the exact order of the nonadaptive system is not required, so, as to eliminate the identification problem. The applicability of the mentioned technique (DPT) was examined through the solution of several problems. This article introduces the solution of a third order system with three adjustable parameters, controlled according to second order reference model. The adjustable parameters have great initial error which represent condition. Computer simulations for the solution and analysis are provided to demonstrate the simplicity and feasibility of the technique.

Keywords: Adaptive Control System, Discrete Parameter Tracking, Discrete Time Model.

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Authors: Ni Hong, Wu Guobin, Wu Gang, Pan Liang

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Interactive push VOD system is a new kind of system that incorporates push technology and interactive technique. It can push movies to users at high speeds at off-peak hours for optimal network usage so as to save bandwidth. This paper presents effective software-based solution for processing mass downstream data at terminals of interactive push VOD system, where the service can download movie according to a viewer-s selection. The downstream data is divided into two catalogs: (1) the carousel data delivered according to DSM-CC protocol; (2) IP data delivered according to Euro-DOCSIS protocol. In order to accelerate download speed and reduce data loss rate at terminals, this software strategy introduces caching, multi-thread and resuming mechanisms. The experiments demonstrate advantages of the software-based solution.

Keywords: DSM-CC, data carousel, Euro-DOCSIS, push VOD.

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Authors: Chenxi Yang, Zhouhong Li

Abstract:

This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.

Keywords: Permanence, Almost periodic solution, Epidemic model, Delay, Feedback control.

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Authors: Lalit Garg, Sally McClean, Maria Barton

Abstract:

Healthcare issues continue to pose huge problems and incur massive costs. As a result there are many challenging problems still unresolved. In this paper, we will carry out an extensive scientific survey of different areas of management and planning in an attempt to identify where there has already been a substantial contribution from management science methods to healthcare problems and where there is a clear potential for more work to be done. The focus will be on the read-across to the healthcare domain from such approaches applied generally to management and planning and how the methods can be used to improvement patient care. We conclude that, since the healthcare domain significantly differs from traditional areas of management and planning, in some cases there is a need to modify the approaches so as to incorporate the complexities of healthcare, and fully exploit the potential for improvement.

Keywords: Management science, management and planning, transforming services, healthcare.

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Authors: Aytunc Durlanik, Ibrahim Sogukpinar

Abstract:

SIP (Session Initiation Protocol), using HTML based call control messaging which is quite simple and efficient, is being replaced for VoIP networks recently. As for authentication and authorization purposes there are many approaches and considerations for securing SIP to eliminate forgery on the integrity of SIP messages. On the other hand Elliptic Curve Cryptography has significant advantages like smaller key sizes, faster computations on behalf of other Public Key Cryptography (PKC) systems that obtain data transmission more secure and efficient. In this work a new approach is proposed for secure SIP authentication by using a public key exchange mechanism using ECC. Total execution times and memory requirements of proposed scheme have been improved in comparison with non-elliptic approaches by adopting elliptic-based key exchange mechanism.

Keywords: SIP, Elliptic Curve Cryptography, voice over IP.

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Authors: B. Guezzen, M. A. Didi, B. Medjahed

Abstract:

An organoclay (HDTMA-B) was prepared from sodium bentonite (Na-B). The starting material was modified using the hexadecyltrimethylammonium ion (HDTMA⁺) in the amounts corresponding to 100 % of the CEC value. Batch experiments were carried out in order to model and optimize the sorption of Congo red dye from aqueous solution. The pseudo-first order and pseudo-second order kinetic models have been developed to predict the rate constant and the sorption capacity at equilibrium with the effect of temperature, the solid/solution ratio and the initial dye concentration. The equilibrium time was reached within 60 min. At room temperature (20 °C), optimum dye sorption of 49.4 mg/g (98.9%) was achieved at pH 6.6, sorbent dosage of 1g/L and initial dye concentration of 50 mg/L, using surfactant modified bentonite. The optimization of adsorption parameters mentioned above on dye removal was carried out using Box-Behnken design. The sorption parameters were analyzed statistically by means of variance analysis by using the Statgraphics Centurion XVI software.

Keywords: Adsorption, dye, factorial design, kinetic, organo-bentonite.

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

Abstract:

The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.

Keywords: Base-isolated structures, earthquake engineering, mixed time integration, nonlinear exponential model.

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Authors: Monjed Ezzeddinne, Nicolas Lefebvre, Régis Lengellé

Abstract:

This paper presents a new version of the SVM mixture algorithm initially proposed by Kwok for classification and regression problems. For both cases, a slight modification of the mixture model leads to a standard SVM training problem, to the existence of an exact solution and allows the direct use of well known decomposition and working set selection algorithms. Only the regression case is considered in this paper but classification has been addressed in a very similar way. This method has been successfully applied to engine pollutants emission modeling.

Keywords: Identification, Learning systems, Mixture ofExperts, Support Vector Machines.

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Authors: Marta Czyżewska, Krzysztof Pancerz, Jarosław Szkoła

Abstract:

The aim of this paper is to assess the influence of several indicators determining innovativeness of countries' economies by applying selected soft computing methods. Such methods enable us to identify correlations between indicators for period 2006-2010. The main attention in the paper is focused on selecting proper computer tools for solving this problem. As a tool supporting identification, the X-means clustering algorithm, the Apriori rules generation algorithm as well as Self-Organizing Feature Maps (SOMs) have been selected. The paper has rather a rudimentary character. We briefly describe usefulness of the selected approaches and indicate some challenges for further research.

Keywords: Assessment of indicators, innovativeness, soft computing.

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Authors: Shao-Tzu Huang, Chen-Chien Hsu, Wei-Yen Wang

Abstract:

Matching high dimensional features between images is computationally expensive for exhaustive search approaches in computer vision. Although the dimension of the feature can be degraded by simplifying the prior knowledge of homography, matching accuracy may degrade as a tradeoff. In this paper, we present a feature matching method based on k-means algorithm that reduces the matching cost and matches the features between images instead of using a simplified geometric assumption. Experimental results show that the proposed method outperforms the previous linear exhaustive search approaches in terms of the inlier ratio of matched pairs.

Keywords: Feature matching, k-means clustering, scale invariant feature transform, linear exhaustive search.

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Authors: Soottipoom Yaowiwat, Manoj Lohatepanont, Proadpran Punyabukkana

Abstract:

Several approaches such as linear programming, network modeling, greedy heuristic and decision support system are well-known approaches in solving irregular airline operation problem. This paper presents an alternative approach based on Multi Objective Micro Genetic Algorithm. The aim of this research is to introduce the concept of Multi Objective Micro Genetic Algorithm as a tool to solve irregular airline operation, combine and reroute problem. The experiment result indicated that the model could obtain optimal solutions within a few second.

Keywords: Irregular Airline Operation, Combine and RerouteRoutine, Genetic Algorithm, Micro Genetic Algorithm, Multi ObjectiveOptimization, Evolutionary Algorithm.

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Authors: R. Sharma, M. Gopal

Abstract:

This paper presents a new problem solving approach that is able to generate optimal policy solution for finite-state stochastic sequential decision-making problems with high data efficiency. The proposed algorithm iteratively builds and improves an approximate Markov Decision Process (MDP) model along with cost-to-go value approximates by generating finite length trajectories through the state-space. The approach creates a synergy between an approximate evolving model and approximate cost-to-go values to produce a sequence of improving policies finally converging to the optimal policy through an intelligent and structured search of the policy space. The approach modifies the policy update step of the policy iteration so as to result in a speedy and stable convergence to the optimal policy. We apply the algorithm to a non-holonomic mobile robot control problem and compare its performance with other Reinforcement Learning (RL) approaches, e.g., a) Q-learning, b) Watkins Q(λ), c) SARSA(λ).

Keywords: Markov Decision Process (MDP), Mobile robot, Policy iteration, Simulation.

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Authors: Hamed Harrafi, Masoumeh Khedri, Karim Karaminejad

Abstract:

Measurement of the COD of a spent caustic solution involves firstly digestion of a test sample with dichromate solution and secondly measurement of dichromate remained by titration by ferrous ammonium sulfate [FAS] to an end point. In this paper we study by a potentiometric end point with Ag/AgCl reference electrode and gold rode electrode. The potentiometric end point is sharp and easily identified especially for the samples with high turbidity and color that other methods such as colorimetric in this type of sample do not result in high precision. Because interim of titration responds quickly to potential changes within the [Cr+6/Cr+3& Fe+2/Fe+3] solution producing stable readings that is lead to accurate COD measurement. Finally results are compared with data determined using colorimetric method for standard samples. It is shown that the potentiometric end point titration with gold rode electrode can be used with equal or better facility

Keywords: chemical oxygen demand, spent caustic and potentiometric determination

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Authors: N. S. Achour, M. Hamdaoui, S. Ben Nasrallah

Abstract:

Wicking and evaporation of water in porous knitted fabrics is investigated by combining experimental and analytical approaches: The standard wicking model from Lucas and Washburn is enhanced to account for evaporation and gravity effects. The goal is to model the effect of gravity and evaporation on wicking using simple analytical expressions and investigate the influence of fabrics geometrical parameters, such as porosity and thickness on evaporation impact on maximum reachable height values. The results show that fabric properties have a significant influence on evaporation effect. In this paper, an experimental study of determining water kinetics from different knitted fabrics were gravimetrically investigated permitting the measure of the mass and the height of liquid rising in fabrics in various atmospheric conditions. From these measurements, characteristic pore parameters (capillary radius and permeability) can be determined.

Keywords: Evaporation, experimental study, geometrical parameters, model, porous knitted fabrics, wicking.

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Authors: Samira Jebahi, Hassane Oudadesse, Eric Wers, Jiheun Elleuch, Hafedh Elfekih, Hassib Keskes, Xuan Vuong Bui, Abdelfatteh Elfeki

Abstract:

Chitosan (CH) material reinforced by bioactive glass (46S6) was fabricated. 46S6 containing 17% wt% CH was studied in vitro and in vivo. Physicochemical techniques, such as Fourier transform infrared spectroscopy (FT-IR), coupled plasma optical emission spectrometry (ICP-OES) analysis were used. The behavior of 46S6CH17 was studied by measuring the in situ pH in a SBF solution. The 46S6CH17 was implanted in the rat femoral condyl. In vitro 46S6CH17 gave an FTIR - spectrum in which three absorption bands with the maxima at 565, 603 and 1039cm-1 after 3 days of soaking in physiological solution. They are assigned to stretching vibrations of PO4^3- group in phosphate crystalline. Moreover, the pH measurement was decreased in the SBF solution. The stability of the calcium phosphate precipitation depended on the pH value. In vivo, a rise in the Ca and phosphate P ions concentrations in the implanted microenvironment was determined.

Keywords: Bioglass, Chitosan, pH measurement, Hydroxyapatite Carbonateted Layer.

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Authors: Teodora Bakardjieva, Galya Gercheva

Abstract:

In this paper an open agent-based modular framework for personalized and adaptive curriculum generation in e-learning environment is proposed. Agent-based approaches offer several potential advantages over alternative approaches. Agent-based systems exhibit high levels of flexibility and robustness in dynamic or unpredictable environments by virtue of their intrinsic autonomy. The presented framework enables integration of different types of expert agents, various kinds of learning objects and user modeling techniques. It creates possibilities for adaptive e-learning process. The KM e-learning system is in a process of implementation in Varna Free University and will be used for supporting the educational process at the University.

Keywords: agents, e-Learning, knowledge management, knowledge sharing, artificial intelligence

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Authors: N. Mamode Khan, V. Jowaheer

Abstract:

In this paper, we apply and compare two generalized estimating equation approaches to the analysis of car breakdowns data in Mauritius. Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observation as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use the two types of quasi-likelihood estimation approaches to estimate the parameters of the model: marginal and joint generalized quasi-likelihood estimating equation approaches. Under-dispersion parameter is estimated to be around 2.14 justifying the appropriateness of Com-Poisson distribution in modelling underdispersed count responses recorded in this study.

Keywords: Breakdowns, under-dispersion, com-poisson, generalized linear model, marginal quasi-likelihood estimation, joint quasi-likelihood estimation.

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Authors: H. Nikzad, S. Yoshitomi

Abstract:

This study investigates and develops the structural optimization method. The effect of size constraints on practical solution of reinforced concrete (RC) building structure with shear wall is proposed. Cross-sections of beam and column, and thickness of shear wall are considered as design variables. The objective function to be minimized is total cost of the structure by using a simple and efficient automated MATLAB platform structural optimization methodology. With modification of mathematical formulations, the result is compared with optimal solution without size constraints. The most suitable combination of section sizes is selected as for the final design application based on linear static analysis. The findings of this study show that defining higher value of upper bound of sectional sizes significantly affects optimal solution, and defining of size constraints play a vital role in finding of global and practical solution during optimization procedures. The result and effectiveness of proposed method confirm the ability and efficiency of optimal solutions for 3D RC shear wall-frame structure.

Keywords: Structural optimization, linear static analysis, ETABS, MATLAB, RC shear wall-frame structures.

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Authors: Andrus Pedai, Igor Astrov

Abstract:

The focus of this paper is to compare common approaches for Systems of Innovation (SI) and identify proactive alternatives for driving the innovation. Proactive approaches will also consider short and medium term perspectives with developments in the field of Computer Technology and Artificial Intelligence. Concerning Computer Technology and Large Connected Information Systems, it is reasonable to predict that during current or the next century intelligence and innovation will be separated from the constraints of human driven management. After this happens, humans will be no longer driving the innovation and there is possibility that SI for new intelligent systems will set its own targets and exclude humans. Over long time scale these developments could result in scenario, which will lead to the development of larger, cross galactic (universal) proactive SI and Intelligence.

Keywords: Artificial intelligence, DARPA, Moore’s law, proactive innovation, singularity, systems of innovation.

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Authors: Aníbal Rodríguez Fuentes, Juan V. Lorenzo Ginori, Ricardo Grau Ábalo

Abstract:

Identifying protein coding regions in DNA sequences is a basic step in the location of genes. Several approaches based on signal processing tools have been applied to solve this problem, trying to achieve more accurate predictions. This paper presents a new predictor that improves the efficacy of three techniques that use the Fourier Transform to predict coding regions, and that could be computed using an algorithm that reduces the computation load. Some ideas about the combination of the predictor with other methods are discussed. ROC curves are used to demonstrate the efficacy of the proposed predictor, based on the computation of 25 DNA sequences from three different organisms.

Keywords: Bioinformatics, Coding region prediction, Computational load reduction, Digital Signal Processing, Fourier Transform.

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Authors: Mehdi Amoui, Mohammad Zarafshan, Caro Lucas

Abstract:

In spite of all advancement in software testing, debugging remains a labor-intensive, manual, time consuming, and error prone process. A candidate solution to enhance debugging process is to fuse it with testing process. To achieve this integration, a possible solution may be categorizing common software tests and errors followed by the effort on fixing the errors through general solutions for each test/error pair. Our approach to address this issue is based on Christopher Alexander-s pattern and pattern language concepts. The patterns in this language are grouped into three major sections and connect the three concepts of test, error, and debug. These patterns and their hierarchical relationship shape a pattern language that introduces a solution to solve software errors in a known testing context. Finally, we will introduce our developed framework ADE as a sample implementation to support a pattern of proposed language, which aims to automate the whole process of evolving software design via evolutionary methods.

Keywords: Coding Errors, Software debugging, Testing, Patterns, Pattern Language

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Authors: Jing Meng, Peiyong Zhu, Houbiao Li

Abstract:

Many problems in science and engineering field require the solution of shifted linear systems with multiple right hand sides and multiple shifts. To solve such systems efficiently, the implicitly restarted global GMRES algorithm is extended in this paper. However, the shift invariant property could no longer hold over the augmented global Krylov subspace due to adding the harmonic Ritz matrices. To remedy this situation, we enforce the collinearity condition on the shifted system and propose shift implicitly restarted global GMRES. The new method not only improves the convergence but also has a potential to simultaneously compute approximate solution for the shifted systems using only as many matrix vector multiplications as the solution of the seed system requires. In addition, some numerical experiments also confirm the effectiveness of our method.

Keywords: Shifted linear systems, global Krylov subspace, GLGMRESIR, GLGMRESIRsh, harmonic Ritz matrix, harmonic Ritz vector.

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