Search results for: Matrix decomposition

Authors: Khalide Jbilou

Abstract:

In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.

Keywords: IEEEtran, journal, LATEX, paper, template.

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Authors: Guangbin Wang, Xue Li, Fuping Tan

Abstract:

In this paper, we present some new upper bounds for the spectral radius of iterative matrices based on the concept of doubly α diagonally dominant matrix. And subsequently, we give two examples to show that our results are better than the earlier ones.

Keywords: doubly α diagonally dominant matrix, eigenvalue, iterative matrix, spectral radius, upper bound.

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Authors: Stefan Menzel

Abstract:

As a result of the daily workflow in the design development departments of companies, databases containing huge numbers of 3D geometric models are generated. According to the given problem engineers create CAD drawings based on their design ideas and evaluate the performance of the resulting design, e.g. by computational simulations. Usually, new geometries are built either by utilizing and modifying sets of existing components or by adding single newly designed parts to a more complex design. The present paper addresses the two facets of acquiring components from large design databases automatically and providing a reasonable overview of the parts to the engineer. A unified framework based on the topographic non-negative matrix factorization (TNMF) is proposed which solves both aspects simultaneously. First, on a given database meaningful components are extracted into a parts-based representation in an unsupervised manner. Second, the extracted components are organized and visualized on square-lattice 2D maps. It is shown on the example of turbine-like geometries that these maps efficiently provide a wellstructured overview on the database content and, at the same time, define a measure for spatial similarity allowing an easy access and reuse of components in the process of design development.

Keywords: Design decomposition, topographic non-negative matrix factorization, parts-based representation, self-organization, unsupervised feature extraction.

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Authors: Ivica Martinjak, Mario-Osvin Pavcevic

Abstract:

When trying to enumerate all BIBD-s for given parameters, their natural solution space appears to be huge and grows extremely with the number of points of the design. Therefore, constructive enumerations are often carried out by assuming additional constraints on design-s structure, automorphisms being mostly used ones. It remains a hard task to construct designs with trivial automorphism group – those with no additional symmetry – although it is believed that most of the BIBD-s belong to that case. In this paper, very many new designs with parameters 2-(13, 5, 5), 2-(16, 6, 5) and 2-(21, 6, 4) are constructed, assuming an action of an automorphism of order 3. Even more, it was possible to construct millions of such designs with no non-trivial automorphisms.

Keywords: BIBD, incidence matrix, automorphism group, tactical decomposition, deterministic algorithm.

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Authors: Guangbin Wang, Liangliang Li, Fuping Tan

Abstract:

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

Keywords: Generalized alternating two-stage method, linear system, convergence.

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Chuan Li, Ming Liang

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Oil debris signal generated from the inductive oil debris monitor (ODM) is useful information for machine condition monitoring but is often spoiled by background noise. To improve the reliability in machine condition monitoring, the high-fidelity signal has to be recovered from the noisy raw data. Considering that the noise components with large amplitude often have higher frequency than that of the oil debris signal, the integral transform is proposed to enhance the detectability of the oil debris signal. To cancel out the baseline wander resulting from the integral transform, the empirical mode decomposition (EMD) method is employed to identify the trend components. An optimal reconstruction strategy including both de-trending and de-noising is presented to detect the oil debris signal with less distortion. The proposed approach is applied to detect the oil debris signal in the raw data collected from an experimental setup. The result demonstrates that this approach is able to detect the weak oil debris signal with acceptable distortion from noisy raw data.

Keywords: Integral transform, empirical mode decomposition, oil debris, signal processing, detection.

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Authors: Q. Z. Yang, B. H. Chua, B. Song

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Technology assessment is a vital part of decision process in manufacturing, particularly for decisions on selection of new sustainable manufacturing processes. To assess these processes, a matrix approach is introduced and sustainability assessment models are developed. Case studies show that the matrix-based approach provides a flexible and practical way for sustainability evaluation of new manufacturing technologies such as those used in surface coating. The technology assessment of coating processes reveals that compared with powder coating, the sol-gel coating can deliver better technical, economical and environmental sustainability with respect to the selected sustainability evaluation criteria for a decorative coating application of car wheels.

Keywords: Evaluation matrix, sustainable manufacturing, surface coating, technology assessment

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Authors: Phuoc Si Nguyen

Abstract:

Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: Frequency transformation, Bilinear z-transformation, Pre-warping frequency, Digital filters, Analog filters, Pascal’s triangle.

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Authors: Rafał Adamczak

Abstract:

State-of-the-art methods for secondary structure (Porter, Psi-PRED, SAM-T99sec, Sable) and solvent accessibility (Sable, ACCpro) predictions use evolutionary profiles represented by the position specific scoring matrix (PSSM). It has been demonstrated that evolutionary profiles are the most important features in the feature space for these predictions. Unfortunately applying PSSM matrix leads to high dimensional feature spaces that may create problems with parameter optimization and generalization. Several recently published suggested that applying feature extraction for the PSSM matrix may result in improvements in secondary structure predictions. However, none of the top performing methods considered here utilizes dimensionality reduction to improve generalization. In the present study, we used simple and fast methods for features selection (t-statistics, information gain) that allow us to decrease the dimensionality of PSSM matrix by 75% and improve generalization in the case of secondary structure prediction compared to the Sable server.

Keywords: Secondary structure prediction, feature selection, position specific scoring matrix.

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Authors: J. Cheeneebash, V. Beeharry, A. Gopaul

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The aim of this paper is to express the input-output matrix as a linear ordering problem which is classified as an NP-hard problem. We then use a Tabu search algorithm to find the best permutation among sectors in the input-output matrix that will give an optimal solution. This optimal permutation can be useful in designing policies and strategies for economists and government in their goal of maximizing the gross domestic product.

Keywords: Input-Output matrix, linear ordering problem, Tabusearch.

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Authors: Maleika Heenaye- Mamode Khan , Naushad Mamode Khan, Raja K.Subramanian

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Dorsal hand vein pattern is an emerging biometric which is attracting the attention of researchers, of late. Research is being carried out on existing techniques in the hope of improving them or finding more efficient ones. In this work, Principle Component Analysis (PCA) , which is a successful method, originally applied on face biometric is being modified using Cholesky decomposition and Lanczos algorithm to extract the dorsal hand vein features. This modified technique decreases the number of computation and hence decreases the processing time. The eigenveins were successfully computed and projected onto the vein space. The system was tested on a database of 200 images and using a threshold value of 0.9 to obtain the False Acceptance Rate (FAR) and False Rejection Rate (FRR). This modified algorithm is desirable when developing biometric security system since it significantly decreases the matching time.

Keywords: Dorsal hand vein pattern, PCA, Cholesky decomposition, Lanczos algorithm.

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Authors: Jing Wu, Wei Lv, Yibing Li, Yuanfan You

Abstract:

The separation of speech signals has become a research hotspot in the field of signal processing in recent years. It has many applications and influences in teleconferencing, hearing aids, speech recognition of machines and so on. The sounds received are usually noisy. The issue of identifying the sounds of interest and obtaining clear sounds in such an environment becomes a problem worth exploring, that is, the problem of blind source separation. This paper focuses on the under-determined blind source separation (UBSS). Sparse component analysis is generally used for the problem of under-determined blind source separation. The method is mainly divided into two parts. Firstly, the clustering algorithm is used to estimate the mixing matrix according to the observed signals. Then the signal is separated based on the known mixing matrix. In this paper, the problem of mixing matrix estimation is studied. This paper proposes an improved algorithm to estimate the mixing matrix for speech signals in the UBSS model. The traditional potential algorithm is not accurate for the mixing matrix estimation, especially for low signal-to noise ratio (SNR).In response to this problem, this paper considers the idea of an improved potential function method to estimate the mixing matrix. The algorithm not only avoids the inuence of insufficient prior information in traditional clustering algorithm, but also improves the estimation accuracy of mixing matrix. This paper takes the mixing of four speech signals into two channels as an example. The results of simulations show that the approach in this paper not only improves the accuracy of estimation, but also applies to any mixing matrix.

Keywords: Clustering algorithm, potential function, speech signal, the UBSS model.

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Authors: F. Mehran

Abstract:

In this paper, we study a class of serially concatenated block codes (SCBC) based on matrix interleavers, to be employed in fixed wireless communication systems. The performances of SCBC¬coded systems are investigated under various interleaver dimensions. Numerical results reveal that the matrix interleaver could be a competitive candidate over conventional block interleaver for frame lengths of 200 bits; hence, the SCBC coding based on matrix interleaver is a promising technique to be employed for speech transmission applications in many international standards such as pan-European Global System for Mobile communications (GSM), Digital Cellular Systems (DCS) 1800, and Joint Detection Code Division Multiple Access (JD-CDMA) mobile radio systems, where the speech frame contains around 200 bits.

Keywords: Matrix Interleaver, serial concatenated block codes (SCBC), turbo codes, wireless communications.

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Authors: Aiman Elragig, Hanan Dreiwi, Dung Ly, Idriss Elmabrook

Abstract:

This paper highlights a new approach to look at online principle components analysis (OPCA). Given a data matrix X ∈ R,^m x n we characterise the online updates of its covariance as a matrix perturbation problem. Up to the principle components, it turns out that online updates of the batch PCA can be captured by symmetric matrix perturbation of the batch covariance matrix. We have shown that as n→ n0 >> 1, the batch covariance and its update become almost similar. Finally, utilize our new setup of online updates to find a bound on the angle distance of the principle components of X and its update.

Keywords: Online data updates, covariance matrix, online principle component analysis (OPCA), matrix perturbation.

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Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new method for solving the matrix equation AXB=F . The new method can be considered as a generalized form of the well-known global full orthogonalization method (Gl-FOM) for solving multiple linear systems. Hence, the method will be called extended Gl-FOM (EGl- FOM). For implementing EGl-FOM, generalized forms of block Krylov subspace and global Arnoldi process are presented. Finally, some numerical experiments are given to illustrate the efficiency of our new method.

Keywords: Matrix equations, Iterative methods, Block Krylovsubspace methods.

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Authors: Qiong Huang, Satish Chand

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This paper uses a primary data from 670 Chinese manufacturing firms, together with the newly introduced regressionbased inequality decomposition method, to study the effect of openness on wage inequality. We find that openness leads to a positive industry wage premium, but its contribution to firm-level wage inequality is relatively small, only 4.69%. The major contributor to wage inequality is human capital, which could explain 14.3% of wage inequality across sample firms.  

Keywords: Openness, human capital, wage inequality, decomposition; China.

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Authors: J. Geiser, R. Röhle

Abstract:

In this paper we present discretization and decomposition methods for a multi-component transport model of a chemical vapor deposition (CVD) process. CVD processes are used to manufacture deposition layers or bulk materials. In our transport model we simulate the deposition of thin layers. The microscopic model is based on the heavy particles, which are derived by approximately solving a linearized multicomponent Boltzmann equation. For the drift-process of the particles we propose diffusionreaction equations as well as for the effects of heat conduction. We concentrate on solving the diffusion-reaction equation with analytical and numerical methods. For the chemical processes, modelled with reaction equations, we propose decomposition methods and decouple the multi-component models to simpler systems of differential equations. In the numerical experiments we present the computational results of our proposed models.

Keywords: Chemical reactions, chemical vapor deposition, convection-diffusion-reaction equations, decomposition methods, multi-component transport.

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Authors: Changchun Shen, Shouming Zhong

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This paper investigates the problem of absolute stability and robust stability of a class of Lur-e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the considered systems. To obtain less conservative stability conditions, an operator is defined to construct the Lyapunov functional. Also, the free weighting matrices approach combining a matrix inequality technique is used to reduce the entailed conservativeness. Numerical examples are given to indicate significant improvements over some existing results.

Keywords: Lur'e system, linear matrix inequalities, Lyapunov, stability.

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Authors: Halil Snopce, Ilir Spahiu

Abstract:

In this paper is investigated a possible optimization of some linear algebra problems which can be solved by parallel processing using the special arrays called systolic arrays. In this paper are used some special types of transformations for the designing of these arrays. We show the characteristics of these arrays. The main focus is on discussing the advantages of these arrays in parallel computation of matrix product, with special approach to the designing of systolic array for matrix multiplication. Multiplication of large matrices requires a lot of computational time and its complexity is O(n3 ). There are developed many algorithms (both sequential and parallel) with the purpose of minimizing the time of calculations. Systolic arrays are good suited for this purpose. In this paper we show that using an appropriate transformation implicates in finding more optimal arrays for doing the calculations of this type.

Keywords: Data dependences, matrix multiplication, systolicarray, transformation matrix.

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Authors: Mohammad Tahaye Abadi

Abstract:

The present paper concerns with the influence of fiber packing on the transverse plastic properties of metal matrix composites. A micromechanical modeling procedure is used to predict the effective mechanical properties of composite materials at large tensile and compressive deformations. Microstructure is represented by a repeating unit cell (RUC). Two fiber arrays are considered including ideal square fiber packing and random fiber packing defined by random sequential algorithm. The micromechanical modeling procedure is implemented for graphite/aluminum metal matrix composite in which the reinforcement behaves as elastic, isotropic solids and the matrix is modeled as an isotropic elastic-plastic solid following the von Mises criterion with isotropic hardening and the Ramberg-Osgood relationship between equivalent true stress and logarithmic strain. The deformation is increased to a considerable value to evaluate both elastic and plastic behaviors of metal matrix composites. The yields strength and true elastic-plastic stress are determined for graphite/aluminum composites.

Keywords: Fiber packing, metal matrix composites, micromechanics, plastic deformation, random

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Authors: Weizhi Xu, Zhiyong Liu, Dongrui Fan, Shuai Jiao, Xiaochun Ye, Fenglong Song, Chenggang Yan

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Many-core GPUs provide high computing ability and substantial bandwidth; however, optimizing irregular applications like SpMV on GPUs becomes a difficult but meaningful task. In this paper, we propose a novel method to improve the performance of SpMV on GPUs. A new storage format called HYB-R is proposed to exploit GPU architecture more efficiently. The COO portion of the matrix is partitioned recursively into a ELL portion and a COO portion in the process of creating HYB-R format to ensure that there are as many non-zeros as possible in ELL format. The method of partitioning the matrix is an important problem for HYB-R kernel, so we also try to tune the parameters to partition the matrix for higher performance. Experimental results show that our method can get better performance than the fastest kernel (HYB) in NVIDIA-s SpMV library with as high as 17% speedup.

Keywords: GPU, HYB-R, Many-core, Performance Tuning, SpMV

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Authors: Jing Wu

Abstract:

In this paper, we discuss semiconvergence of the alternating iterative methods for solving singular systems. The semiconvergence theories for the alternating methods are established when the coefficient matrix is a singular matrix. Furthermore, the corresponding comparison theorems are obtained.

Keywords: Alternating iterative method, Semiconvergence, Singular matrix.

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Authors: Sushil Kumar Saraswat, K. K. Pant

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Co metal supported on SiO2 and Al2O3 catalysts with a metal loading varied from 30 of 70 wt.% were evaluated for decomposition of methane to COx free hydrogen and carbon nanomaterials. The catalytic runs were carried out from 550-800oC under atmospheric pressure using fixed bed vertical flow reactor. The fresh and spent catalysts were characterized by BET surface area analyzer, XRD, SEM, TEM and TG analysis. The data showed that 50% Co/Al2O3 catalyst exhibited remarkable higher activity at 800oC with respect to H2 production compared to rest of the catalysts. However, the catalytic activity and durability was greatly declined at higher temperature. The main reason for the catalytic inhibition of Co containing SiO2 catalysts is the higher reduction temperature of Co2SiO4. TEM images illustrate that the carbon materials with various morphologies, carbon nanofibers (CNFs), helical-shaped CNFs and branched CNFs depending on the catalyst composition and reaction temperature were obtained.

Keywords: Carbon nanotubes, Cobalt, Hydrogen Production, Methane decomposition.

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Authors: Omid Ghasemalizadeh, Mohammad Reza Mirzaee, Hossein Sadeghi, Mohammad Taghi Ahmadian

Abstract:

There are lots of different ways to find the natural frequencies of a rotating system. One of the most effective methods which is used because of its precision and correctness is the application of the transfer matrix. By use of this method the entire continuous system is subdivided and the corresponding differential equation can be stated in matrix form. So to analyze shaft that is this paper issue the rotor is divided as several elements along the shaft which each one has its own mass and moment of inertia, which this work would create possibility of defining the named matrix. By Choosing more elements number, the size of matrix would become larger and as a result more accurate answers would be earned. In this paper the dynamics of a rotor-bearing system is analyzed, considering the gyroscopic effect. To increase the accuracy of modeling the thickness of the disk and bearings is also taken into account which would cause more complicated matrix to be solved. Entering these parameters to our modeling would change the results completely that these differences are shown in the results. As said upper, to define transfer matrix to reach the natural frequencies of probed system, introducing some elements would be one of the requirements. For the boundary condition of these elements, bearings at the end of the shaft are modeled as equivalent spring and dampers for the discretized system. Also, continuous model is used for the shaft in the system. By above considerations and using transfer matrix, exact results are taken from the calculations. Results Show that, by increasing thickness of the bearing the amplitude of vibration would decrease, but obviously the stiffness of the shaft and the natural frequencies of the system would accompany growth. Consequently it is easily understood that ignoring the influences of bearing and disk thicknesses would results not real answers.

Keywords: Rotor System, Disk and Bearing Thickness, Transfer Matrix, Amplitude.

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Authors: Ion-Cosmin Dita, Vasile Gui, Franz Quint, Marius Otesteanu

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In automatic manufacturing and assembling of mechanical, electrical and electronic parts one needs to reliably identify the position of components and to extract the information of these components. Data Matrix Codes (DMC) are established by these days in many areas of industrial manufacturing thanks to their concentration of information on small spaces. In today’s usually order-related industry, where increased tracing requirements prevail, they offer further advantages over other identification systems. This underlines in an impressive way the necessity of a robust code reading system for detecting DMC on the components in factories. This paper compares two methods for estimating the angle of orientation of Data Matrix Codes: one method based on the Hough Transform and the other based on the Mean Shift Algorithm. We concentrate on Data Matrix Codes in industrial environment, punched, milled, lasered or etched on different materials in arbitrary orientation.

Keywords: Industrial data matrix code, Hough transform, mean shift.

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Authors: F. F. Howard, C. B. Boye, I. Yakubu, J. S. Y. Kuma

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One of the ways that could be used for the production of land use and land cover maps by a procedure known as image classification is the use of the remote sensing technique. Numerous elements ought to be taken into consideration, including the availability of highly satisfactory Landsat imagery, secondary data and a precise classification process. The goal of this study was to classify and map the land use and land cover of the study area using remote sensing and Geospatial Information System (GIS) analysis. The classification was done using Landsat 8 satellite images acquired in December 2020 covering the study area. The Landsat image was downloaded from the USGS. The Landsat image with 30 m resolution was geo-referenced to the WGS_84 datum and Universal Transverse Mercator (UTM) Zone 30N coordinate projection system. A radiometric correction was applied to the image to reduce the noise in the image. This study consists of two sections: the Land Use/Land Cover (LULC) and Accuracy Assessments using the confusion and contingency matrix and the Kappa coefficient. The LULC classifications were vegetation (agriculture) (67.87%), water bodies (0.01%), mining areas (5.24%), forest (26.02%), and settlement (0.88%). The overall accuracy of 97.87% and the kappa coefficient (K) of 97.3% were obtained for the confusion matrix. While an overall accuracy of 95.7% and a Kappa coefficient of 0.947 were obtained for the contingency matrix, the kappa coefficients were rated as substantial; hence, the classified image is fit for further research.

Keywords: Confusion Matrix, contingency matrix, kappa coefficient, land used/ land cover, accuracy assessment.

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Authors: M. Bouri, S. Bourennane

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In this paper, we propose a novel method for subspace estimation used high resolution method without eigendecomposition where the sample Cross-Spectral Matrix (CSM) is replaced by upper triangular matrix obtained from LU factorization. This novel method decreases the computational complexity. The method relies on a recently published result on Rank-Revealing LU (RRLU) factorization. Simulation results demonstrates that the new algorithm outperform the Householder rank-revealing QR (RRQR) factorization method and the MUSIC in the low Signal to Noise Ratio (SNR) scenarios.

Keywords: Factorization, Localization, Matrix, Signalsubspace.

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Authors: Shishen Xie

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In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations

Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations

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Authors: Kerim Emre Öksüz, Mehmet Çevik, A. Enbiya Bozdağ, Ali Özer, Mehmet Simsir

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Metal matrix composites (MMCs) have gained a considerable interest in the last three decades. Conventional powder metallurgy production route often involves the addition of reinforcing phases into the metal matrix directly, which leads to poor wetting behavior between ceramic phase and metal matrix and the segregation of reinforcements. The commonly used elements for ceramic phase formation in iron based MMCs are Ti, Nb, Mo, W, V and C, B. The aim of the present paper is to investigate the effect of sintering temperature and V-B addition on densification, phase development, microstructure, and hardness of Fe–V-B composites (Fe-(5-10) wt. %B – 25 wt. %V alloys) prepared by powder metallurgy process. Metal powder mixes were pressed uniaxial and sintered at different temperatures (ranging from 1300 to 1400ºC) for 1h. The microstructure of the (V, B) Fe composites was studied with the help of high magnification optical microscope and XRD. Experimental results show that (V, B) Fe composites can be produced by conventional powder metallurgy route.

Keywords: Hardness, Metal matrix composite (MMC), Microstructure, Powder Metallurgy.

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