Search results for: local error.

Authors: Qianhua He, Weili Zhou, Aiwu Chen

Abstract:

A sparse representation speech denoising method based on adapted stopping residue error was presented in this paper. Firstly, the cross-correlation between the clean speech spectrum and the noise spectrum was analyzed, and an estimation method was proposed. In the denoising method, an over-complete dictionary of the clean speech power spectrum was learned with the K-singular value decomposition (K-SVD) algorithm. In the sparse representation stage, the stopping residue error was adaptively achieved according to the estimated cross-correlation and the adjusted noise spectrum, and the orthogonal matching pursuit (OMP) approach was applied to reconstruct the clean speech spectrum from the noisy speech. Finally, the clean speech was re-synthesised via the inverse Fourier transform with the reconstructed speech spectrum and the noisy speech phase. The experiment results show that the proposed method outperforms the conventional methods in terms of subjective and objective measure.

Keywords: Speech denoising, sparse representation, K-singular value decomposition, orthogonal matching pursuit.

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Authors: Shahana T. K., Babita R. Jose, K. Poulose Jacob, Sreela Sasi

Abstract:

The modern telecommunication industry demands higher capacity networks with high data rate. Orthogonal frequency division multiplexing (OFDM) is a promising technique for high data rate wireless communications at reasonable complexity in wireless channels. OFDM has been adopted for many types of wireless systems like wireless local area networks such as IEEE 802.11a, and digital audio/video broadcasting (DAB/DVB). The proposed research focuses on a concatenated coding scheme that improve the performance of OFDM based wireless communications. It uses a Redundant Residue Number System (RRNS) code as the outer code and a convolutional code as the inner code. Here, a direct conversion of analog signal to residue domain is done to reduce the conversion complexity using sigma-delta based parallel analog-to-residue converter. The bit error rate (BER) performances of the proposed system under different channel conditions are investigated. These include the effect of additive white Gaussian noise (AWGN), multipath delay spread, peak power clipping and frame start synchronization error. The simulation results show that the proposed RRNS-Convolutional concatenated coding (RCCC) scheme provides significant improvement in the system performance by exploiting the inherent properties of RRNS.

Keywords: Analog-to-residue converter, Concatenated codes, OFDM, Redundant Residue Number System, Sigma-delta modulator, Wireless communication

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Authors: Raghvendra Kumar, Lillie Dewan

Abstract:

Exchange algorithm with constraints on magnitude and phase error separately in new way is presented in this paper. An important feature of the algorithms presented in this paper is that they allow for design constraints which often arise in practical filter design problems. Meeting required minimum stopband attenuation or a maximum deviation from the desired magnitude and phase responses in the passbands are common design constraints that can be handled by the methods proposed here. This new algorithm may have important advantages over existing technique, with respect to the speed and stability of convergence, memory requirement and low ripples.

Keywords: Least square estimation, Constraints, Exchange algorithm.

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Authors: A. Umemuro, M. Sato, M. Narita, S. Hori, S. Sakurai, T. Nakayama, A. Nakazawa, T. Ogura

Abstract:

Mammography requires the detection of very small calcifications, and physicians search for microcalcifications by magnifying the images as they read them. The mouse is necessary to zoom in on the images, but this can be tiring and distracting when many images are read in a single day. Therefore, an image magnification system combining an eye-detector and a simple electroencephalograph (EEG) scanner was devised, and its operability was evaluated. Two experiments were conducted in this study: the measurement of eye-detection error using an eye-detector and the measurement of the time required for image magnification using a simple EEG scanner. Eye-detector validation showed that the mean distance of eye-detection error ranged from 0.64 cm to 2.17 cm, with an overall mean of 1.24 ± 0.81 cm for the observers. The results showed that the eye detection error was small enough for the magnified area of the mammographic image. The average time required for point magnification in the verification of the simple EEG scanner ranged from 5.85 to 16.73 seconds, and individual differences were observed. The reason for this may be that the size of the simple EEG scanner used was not adjustable, so it did not fit well for some subjects. The use of a simple EEG scanner with size adjustment would solve this problem. Therefore, the image magnification system using the eye-detector and the simple EEG scanner is useful.

Keywords: EEG scanner, eye-detector, mammography, observers.

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Authors: Wen-Yuh Jywe, Bor-Jeng Lin, Jing-Chung Shen, Jeng-Dao Lee, Hsueh-Liang Huang, Ming-Chen Cho

Abstract:

The dynamical contouring error is a critical element for the accuracy of machine tools. The contouring error is defined as the difference between the processing actual path and commanded path, which is implemented by following the command curves from feeding driving system in machine tools. The contouring error is resulted from various factors, such as the external loads, friction, inertia moment, feed rate, speed control, servo control, and etc. Thus, the study proposes a 2D compensating system for the contouring accuracy of machine tools. Optical method is adopted by using stable frequency laser diode and the high precision position sensor detector (PSD) to performno-contact measurement. Results show the related accuracy of position sensor detector (PSD) of 2D contouring accuracy compensating system was ±1.5 μm for a calculated range of ±3 mm, and improvement accuracy is over 80% at high-speed feed rate.

Keywords: Position sensor detector, laser diode, contouring accuracy, machine tool.

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Authors: Jaouadi Ikram, Machhout Mohsen

Abstract:

The development of a quantum key distribution (QKD) system on a field-programmable gate array (FPGA) platform is the subject of this paper. A quantum cryptographic protocol is designed based on the properties of quantum information and the characteristics of FPGAs. The proposed protocol performs key extraction, reconciliation, error correction, and privacy amplification tasks to generate a perfectly secret final key. We modeled the presence of the spy in our system with a strategy to reveal some of the exchanged information without being noticed. Using an FPGA card with a 100 MHz clock frequency, we have demonstrated the evolution of the error rate as well as the amounts of mutual information (between the two interlocutors and that of the spy) passing from one step to another in the key generation process.

Keywords: QKD, BB84, protocol, cryptography, FPGA, key, security, communication.

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Authors: Prof. Chokri SLIM

Abstract:

A Novel fuzzy neural network combining with support vector learning mechanism called support-vector-based fuzzy neural networks (SVBFNN) is proposed. The SVBFNN combine the capability of minimizing the empirical risk (training error) and expected risk (testing error) of support vector learning in high dimensional data spaces and the efficient human-like reasoning of FNN.

Keywords: Neural network, fuzzy inference, machine learning, fuzzy modeling and rule extraction, support vector regression.

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Authors: Mohamed El Aroussi, Mohammed El Hassouni, Sanaa Ghouzali, Mohammed Rziza, Driss Aboutajdine

Abstract:

In this paper the problem of face recognition under variable illumination conditions is considered. Most of the works in the literature exhibit good performance under strictly controlled acquisition conditions, but the performance drastically drop when changes in pose and illumination occur, so that recently number of approaches have been proposed to deal with such variability. The aim of this work is to introduce an efficient local appearance feature extraction method based steerable pyramid (SP) for face recognition. Local information is extracted from SP sub-bands using LBP(Local binary Pattern). The underlying statistics allow us to reduce the required amount of data to be stored. The experiments carried out on different face databases confirm the effectiveness of the proposed approach.

Keywords: Face recognition (FR), Steerable pyramid (SP), localBinary Pattern (LBP).

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Authors: Derjew Ayele Ejigu, Houde Song, Xiaojing Liu

Abstract:

This work presents the particle swarm optimization trained neural network (PSO-NN) supervisory proportional integral derivative (PID) control method to monitor the pressurized water reactor (PWR) core power for safe operation. The proposed control approach is implemented on the transfer function of the PWR core, which is computed from the state-space model. The PWR core state-space model is designed from the neutronics, thermal-hydraulics, and reactivity models using perturbation around the equilibrium value. The proposed control approach computes the control rod speed to maneuver the core power to track the reference in a closed-loop scheme. The particle swarm optimization (PSO) algorithm is used to train the neural network (NN) and to tune the PID simultaneously. The controller performance is examined using integral absolute error, integral time absolute error, integral square error, and integral time square error functions, and the stability of the system is analyzed by using the Bode diagram. The simulation results indicated that the controller shows satisfactory performance to control and track the load power effectively and smoothly as compared to the PSO-PID control technique. This study will give benefit to design a supervisory controller for nuclear engineering research fields for control application.

Keywords: machine learning, neural network, pressurized water reactor, supervisory controller

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Authors: Chunguang Wang, Krishna Shankar, Evgeny V. Morozov

Abstract:

The use of composite materials in offshore engineering for deep sea oil production riser systems has drawn considerable interest due to the potential weight savings and improvement in durability. The design of composite risers consists of two stages: (1) local design based on critical local load cases, and (2) global analysis of the full length composite riser under global loads and assessment of critical locations. In the first stage, eight different material combinations were selected and their laminate configurations optimised under local load considerations. Stage two includes a final local stress analysis of the critical sections of the riser under the combined loads determined in the global analysis. This paper describes two design methodologies of the composite riser to provide minimum structural weight and shows that the use of off angle fibre orientations in addition to axial and hoop reinforcements offer substantial weight savings and ensure the structural capacity.

Keywords: Composite Riser, Composite Tubular, Finite Element Modelling, Global Design, Local Design, Offshore Engineering.

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Authors: Somkiat Wangsiripitak

Abstract:

Virtual touch screen using camera is an ordinary screen which uses a camera to imitate the touch screen by taking a picture of an indicator, e.g., finger, which is laid on the screen, converting the indicator tip position on the picture to the position on the screen, and moving the cursor on the screen to that position. In fact, the indicator is not laid on the screen directly, but it is intervened by the cover at some intervals. In spite of this gap, if the eye-indicator-camera angle is not large, the mapping from the indicator tip positions on the image to the corresponding cursor positions on the screen is not difficult and could be done with a little error. However, the larger the angle is, the bigger the error in the mapping occurs. This paper proposes cursor position estimation model for virtual touch screen using camera which could eliminate this kind of error. The proposed model (i) moves the on-screen pilot cursor to the screen position which locates on the screen at the position just behind the indicator tip when the indicator tip has been looked from the camera position, and then (ii) converts that pilot cursor position to the desirable cursor position (the position on the screen when it has been looked from the user-s eye through the indicator tip) by using the bilinear transformation. Simulation results show the correctness of the estimated cursor position by using the proposed model.

Keywords: Bilinear transformation, cursor position, pilot cursor, virtual touch screen.

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Authors: V. Rednic, N. Aldea, P. Marginean, D. Macovei, C. M. Teodorescu, E. Dorolti, F. Matei

Abstract:

The supported Pd catalysts were analyzed by X-ray diffraction and X-ray absorption spectroscopy in order to determine their global and local structure. The average particle size of the supported Pd catalysts was determined by X-ray diffraction method. One of the main purposes of the present contribution is to focus on understanding the specific role of the Pd particle size determined by X-ray diffraction and that of the support oxide. Based on X-ray absorption fine structure spectroscopy analysis we consider that the whole local structure of the investigated samples are distorted concerning the atomic number but the distances between atoms are almost the same as for standard Pd sample. Due to the strong modifications of the Pd cluster local structure, the metal-support interface may influence the electronic properties of metal clusters and thus their reactivity for absorption of the reactant molecules.

Keywords: metal-support interaction, supported metal catalysts, synchrotron radiation, X-ray absorption spectroscopy, X-raydiffraction

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Authors: O. Hashemipour, S. G. Nabavi

Abstract:

A high-linearity and high-speed current-mode sampleand- hold circuit is designed and simulated using a 0.25μm CMOS technology. This circuit design is based on low voltage and it utilizes a fully differential circuit. Due to the use of only two switches the switch related noise has been reduced. Signal - dependent -error is completely eliminated by a new zero voltage switching technique. The circuit has a linearity error equal to ±0.05μa, i.e. 12-bit accuracy with a ±160 μa differential output - input signal frequency of 5MHZ, and sampling frequency of 100 MHZ. Third harmonic is equal to –78dB.

Keywords: Zero-voltage-technique, MOS-resistor, OTA, Feedback-resistor.

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Authors: M. Ouassaid, M. Cherkaoui, A. Nejmi, M. Maaroufi

Abstract:

This study presents a novel means of designing a simple and effective torque controller for Permanent Magnet Synchronous Motor (PMSM). The overall stability of the system is shown using Lyapunov technique. The Lyapunov functions used contain a term penalizing the integral of the tracking error, enhancing the stability. The tracking error is shown to be globally uniformly bounded. Simulation results are presented to show the effectiveness of the approach.

Keywords: Integral action, Lyapunov Technique, Non Linear Control, Permanent Magnet Synchronous Motors, Torque Control, Stability.

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Authors: Phruksaphanrat B.

Abstract:

This research presents a fuzzy multi-objective model for a machine selection problem in a flexible manufacturing system of a tire company. Two main objectives are minimization of an average machine error and minimization of the total setup time. Conventionally, the working team uses trial and error in selecting a pressing machine for each task due to the complexity and constraints of the problem. So, both objectives may not satisfy. Moreover, trial and error takes a lot of time to get the final decision. Therefore, in this research preemptive fuzzy goal programming model is developed for solving this multi-objective problem. The proposed model can obtain the appropriate results that the Decision Making (DM) is satisfied for both objectives. Besides, alternative choice can be easily generated by varying the satisfaction level. Additionally, decision time can be reduced by using the model, which includes all constraints of the system to generate the solutions. A numerical example is also illustrated to show the effectiveness of the proposed model.

Keywords: Machine Selection, Preemptive Fuzzy Goal Programming, Mixed Integer Programming, Application of Tire Industry.

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Authors: Grzegorz Ulacha, Ryszard Stasiński

Abstract:

In the paper an effective context based lossless coding technique is presented. Three principal and few auxiliary contexts are defined. The predictor adaptation technique is an improved CoBALP algorithm, denoted CoBALP+. Cumulated predictor error combining 8 bias estimators is calculated. It is shown experimentally that indeed, the new technique is time-effective while it outperforms the well known methods having reasonable time complexity, and is inferior only to extremely computationally complex ones.

Keywords: Adaptive prediction, context coding, image losslesscoding, prediction error bias correction.

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Authors: Wichian Sriprachan, Chutikarn Sriviboon

Abstract:

The objectives of this research were to study the management of local towns and to develop a better model of town management according to the Philosophy of Sufficiency Economy. This study utilized qualitative research, field research, as well as documentary research at the same time. A total of 10 local towns or Tambons of Supanburi province, Thailand were selected for an in-depth interview. The findings revealed that the model of local town management according to Philosophy of Sufficient Economy was in a level of “good” and the model of management has the five basic guidelines: 1) ability to manage budget information and keep it up-to-date, 2) ability to decision making according to democracy rules, 3) ability to use check and balance system, 4) ability to control, follow, and evaluation, and 5) ability to allow the general public to participate. In addition, the findings also revealed that the human resource management according to Philosophy of Sufficient Economy includes obeying laws, using proper knowledge, and having integrity in five areas: plan, recruit, select, train, and maintain human resources.  

Keywords: Management, Local Town (Tambon), Principles of Sufficiency Economy.

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Authors: P. Pongsumpun

Abstract:

Herpes zoster is a disease that manifests as a dermatological condition. The characteristic of this disease is an irritating skin rash with blisters. This is often limited to one side of body. From the data of Herpes zoster cases in Thailand, we found that age structure effects to the transmission of this disease. In this study, we construct the age structural model of Herpes zoster in Thailand. The local stability analysis of this model is given. The numerical solutions are shown to confirm the analytical results.

Keywords: Age structural model, Herpes zoster, local stability, Numerical solution.

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Authors: Thiyam Tamphasana Devi, Bimlesh Kumar

Abstract:

A Computational Fluid Dynamics (CFD) technique has been applied to simulate the gas-liquid phase in double stirred tank of Rushton impeller. Eulerian-Eulerian model was adopted to simulate the multiphase with standard correlation of Schiller and Naumann for drag co-efficient. The turbulence was modeled by using standard k-ε turbulence model. The present CFD model predicts flow pattern, local gas hold-up, and local specific area. It also predicts local kLa (mass transfer rate) for single impeller. The predicted results were compared with experimental and CFD results of published literature. The predicted results are slightly over predicted with the experimental results; however, it is in reasonable agreement with other simulated results of published literature.

Keywords: Eulerian-Eulerian, gas-hold up, gas-liquid phase, local mass transfer rate, local specific area, Rushton Impeller.

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Authors: Hyung-Weon Cho, Youngyoon Lee, Seung Goo Kang, Dahae Chong, Myungsoo Lee, Chonghan Song, Seokho Yoon

Abstract:

This paper proposes a novel spectrum sensing technique for the digital video broadcasting-terrestrial (DVB-T) systems, which utilizes the periodicity of pilot signals in the orthogonal frequency division multiplexing (OFDM) symbols. The proposed scheme can overcome the effect of the timing synchronization error by recorrelating the correlation values in the same sample distances. The numerical results demonstrate that the detection probability performance of the proposed scheme outperforms that of the conventional scheme when there exists a timing synchronization error.

Keywords: DVB-T, spectrum sensing, OFDM, timing synchronizationerror.

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Authors: Sin Yin Teh, Abdul Rahman Othman, Michael Boon Chong Khoo

Abstract:

In this paper, the concepts of dichotomous logistic regression (DLR) with leave-one-out (L-O-O) were discussed. To illustrate this, the L-O-O was run to determine the importance of the simulation conditions for robust test of spread procedures with good Type I error rates. The resultant model was then evaluated. The discussions included 1) assessment of the accuracy of the model, and 2) parameter estimates. These were presented and illustrated by modeling the relationship between the dichotomous dependent variable (Type I error rates) with a set of independent variables (the simulation conditions). The base SAS software containing PROC LOGISTIC and DATA step functions can be making used to do the DLR analysis.

Keywords: Dichotomous logistic regression, leave-one-out, testof spread.

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Authors: Mahkameh S. Mostafavi

Abstract:

In this paper an algorithm is used to detect the color defects of ceramic tiles. First the image of a normal tile is clustered using GCMA; Genetic C-means Clustering Algorithm; those results in best cluster centers. C-means is a common clustering algorithm which optimizes an objective function, based on a measure between data points and the cluster centers in the data space. Here the objective function describes the mean square error. After finding the best centers, each pixel of the image is assigned to the cluster with closest cluster center. Then, the maximum errors of clusters are computed. For each cluster, max error is the maximum distance between its center and all the pixels which belong to it. After computing errors all the pixels of defected tile image are clustered based on the centers obtained from normal tile image in previous stage. Pixels which their distance from their cluster center is more than the maximum error of that cluster are considered as defected pixels.

Keywords: C-Means algorithm, color spaces, Genetic Algorithm, image clustering.

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Authors: Sebastian B. Mendes

Abstract:

The presence of a vertical fatigue crack in the web of a plate girder subjected to pure bending influences the bending moment capacity of the girder. The growth of the crack may lead to premature elastic failure due to flange local yielding, flange local buckling, or web local buckling. Approximate expressions for the bending moment capacities corresponding to these failure modes were formulated. Finite element analyses were then used to validate the expressions. The expressions were employed to assess the effects of crack length on the capacity. Neglecting brittle fracture, tension buckling, and ductile failure modes, it was found that typical girders are governed by the capacity associated with flange local yielding as influenced by the crack. Concluding, a possible use of the capacity expressions in girder design was demonstrated.

Keywords: Fatigue crack, flange yielding, flange buckling, web buckling.

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Authors: N. Praveen Kumar, Abhijit Mitra, C. Ardil

Abstract:

Decision feedback equalizers are commonly employed to reduce the error caused by intersymbol interference. Here, an adaptive decision feedback equalizer is presented with a new adaptation algorithm. The algorithm follows a block-based approach of normalized least mean square (NLMS) algorithm with set-membership filtering and achieves a significantly less computational complexity over its conventional NLMS counterpart with set-membership filtering. It is shown in the results that the proposed algorithm yields similar type of bit error rate performance over a reasonable signal to noise ratio in comparison with the latter one.

Keywords: Decision feedback equalizer, Adaptive algorithm, Block based computation, Set membership filtering.

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Authors: Abdenour Bounsiar, Edith Grall, Pierre Beauseroy

Abstract:

In this paper we are interested in classification problems with a performance constraint on error probability. In such problems if the constraint cannot be satisfied, then a rejection option is introduced. For binary labelled classification, a number of SVM based methods with rejection option have been proposed over the past few years. All of these methods use two thresholds on the SVM output. However, in previous works, we have shown on synthetic data that using thresholds on the output of the optimal SVM may lead to poor results for classification tasks with performance constraint. In this paper a new method for supervised classification with rejection option is proposed. It consists in two different classifiers jointly optimized to minimize the rejection probability subject to a given constraint on error rate. This method uses a new kernel based linear learning machine that we have recently presented. This learning machine is characterized by its simplicity and high training speed which makes the simultaneous optimization of the two classifiers computationally reasonable. The proposed classification method with rejection option is compared to a SVM based rejection method proposed in recent literature. Experiments show the superiority of the proposed method.

Keywords: rejection, Chow's rule, error-reject tradeoff, SupportVector Machine.

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Authors: Olfa.Ben Ahmed, Mahmoud. Mejdoub, Chokri. Ben Amar

Abstract:

Recognizing human action from videos is an active field of research in computer vision and pattern recognition. Human activity recognition has many potential applications such as video surveillance, human machine interaction, sport videos retrieval and robot navigation. Actually, local descriptors and bag of visuals words models achieve state-of-the-art performance for human action recognition. The main challenge in features description is how to represent efficiently the local motion information. Most of the previous works focus on the extension of 2D local descriptors on 3D ones to describe local information around every interest point. In this paper, we propose a new spatio-temporal descriptor based on a spacetime description of moving points. Our description is focused on an Accordion representation of video which is well-suited to recognize human action from 2D local descriptors without the need to 3D extensions. We use the bag of words approach to represent videos. We quantify 2D local descriptor describing both temporal and spatial features with a good compromise between computational complexity and action recognition rates. We have reached impressive results on publicly available action data set

Keywords: Accordion, Bag of Features, Human action, Motion, Moving point, Space-Time Descriptor, SIFT, Video.

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Authors: Abhijit Mitra, Harpreet Singh Dhillon

Abstract:

We present a novel scheme to evaluate sinusoidal functions with low complexity and high precision using cubic spline interpolation. To this end, two different approaches are proposed to find the interpolating polynomial of sin(x) within the range [- π , π]. The first one deals with only a single data point while the other with two to keep the realization cost as low as possible. An approximation error optimization technique for cubic spline interpolation is introduced next and is shown to increase the interpolator accuracy without increasing complexity of the associated hardware. The architectures for the proposed approaches are also developed, which exhibit flexibility of implementation with low power requirement.

Keywords: Arithmetic, spline interpolator, hardware design, erroranalysis, optimization methods.

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Authors: Nahid Ardalani, Ahmadreza Khoogar, H. Roohi

Abstract:

In this paper we compare the response of linear and nonlinear neural network-based prediction schemes in prediction of received Signal-to-Interference Power Ratio (SIR) in Direct Sequence Code Division Multiple Access (DS/CDMA) systems. The nonlinear predictor is Multilayer Perceptron MLP and the linear predictor is an Adaptive Linear (Adaline) predictor. We solve the problem of complexity by using the Minimum Mean Squared Error (MMSE) principle to select the optimal predictors. The optimized Adaline predictor is compared to optimized MLP by employing noisy Rayleigh fading signals with 1.8 GHZ carrier frequency in an urban environment. The results show that the Adaline predictor can estimates SIR with the same error as MLP when the user has the velocity of 5 km/h and 60 km/h but by increasing the velocity up-to 120 km/h the mean squared error of MLP is two times more than Adaline predictor. This makes the Adaline predictor (with lower complexity) more suitable than MLP for closed-loop power control where efficient and accurate identification of the time-varying inverse dynamics of the multi path fading channel is required.

Keywords: Power control, neural networks, DS/CDMA mobilecommunication systems.

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Authors: Jong-Bae Lee, Seongsoo Lee

Abstract:

Local interconnect network (LIN) is a communication protocol that combines sensors, actuators, and processors to a functional module in automotive applications. In this paper, a LIN ver. 2.2A controller was designed in Verilog hardware description language (Verilog HDL) and implemented in field-programmable gate array (FPGA). Its operation was verified by making full-scale LIN network with the presented FPGA-implemented LIN controller, commercial LIN transceivers, and commercial processors. When described in Verilog HDL and synthesized in 0.18 μm technology, its gate size was about 2,300 gates.

Keywords: Local interconnect network, controller, transceiver, processor.

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Authors: Yang Liu, Jinfeng Wang, Hong Li, Wei Gao, Siriguleng He

Abstract:

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

Keywords: Pseudo-hyperbolic equations, splitting system, H1-Galerkin mixed method, error estimates.

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