The Experts below are selected from a list of 24993 Experts worldwide ranked by ideXlab platform
Gabriel Oksa - One of the best experts on this subject based on the ideXlab platform.
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PPAM (1) - Parallel One–Sided Jacobi SVD Algorithm with Variable Blocking Factor
Parallel Processing and Applied Mathematics, 2014Co-Authors: Martin Becka, Gabriel OksaAbstract:Parallel one-sided block-Jacobi algorithm for the matrix singular value decomposition (SVD) requires an efficient computation of symmetric Gram matrices, their eigenvalue decompositions (EVDs) and an update of matrix columns and right singular vectors by matrix multiplication. In our recent parallel implementation with \(p\) processors and blocking factor \(\ell =2p\), these tasks are computed serially in each processor in a given parallel Iteration Step because each processor contains exactly two block columns of an input matrix \(A\). However, as shown in our previous work, with increasing \(p\) (hence, with increasing blocking factor) the number of parallel Iteration Steps needed for the convergence of the whole algorithm increases linearly but faster than proportionally to \(p\), so that it is hard to achieve a good speedup. We propose to break the tight relation \(\ell =2p\) and to use a small blocking factor \(\ell = p/k\) for some integer \(k\) that divides \(p\), \(\ell \) even. The algorithm then works with pairs of logical block columns that are distributed among processors so that all computations inside a parallel Iteration Step are themselves parallel. We discuss the optimal data distribution for parallel subproblems in the one-sided block-Jacobi algorithm and analyze its computational and communication complexity. Experimental results with full matrices of order \(8192\) show that our new algorithm with a small blocking factor is well scalable and can be \(2\)–\(3\) times faster than the ScaLAPACK procedure PDGESVD.
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parallel one sided jacobi svd algorithm with variable blocking factor
International Conference on Parallel Processing, 2013Co-Authors: Martin Becka, Gabriel OksaAbstract:Parallel one-sided block-Jacobi algorithm for the matrix singular value decomposition (SVD) requires an efficient computation of symmetric Gram matrices, their eigenvalue decompositions (EVDs) and an update of matrix columns and right singular vectors by matrix multiplication. In our recent parallel implementation with \(p\) processors and blocking factor \(\ell =2p\), these tasks are computed serially in each processor in a given parallel Iteration Step because each processor contains exactly two block columns of an input matrix \(A\). However, as shown in our previous work, with increasing \(p\) (hence, with increasing blocking factor) the number of parallel Iteration Steps needed for the convergence of the whole algorithm increases linearly but faster than proportionally to \(p\), so that it is hard to achieve a good speedup. We propose to break the tight relation \(\ell =2p\) and to use a small blocking factor \(\ell = p/k\) for some integer \(k\) that divides \(p\), \(\ell \) even. The algorithm then works with pairs of logical block columns that are distributed among processors so that all computations inside a parallel Iteration Step are themselves parallel. We discuss the optimal data distribution for parallel subproblems in the one-sided block-Jacobi algorithm and analyze its computational and communication complexity. Experimental results with full matrices of order \(8192\) show that our new algorithm with a small blocking factor is well scalable and can be \(2\)–\(3\) times faster than the ScaLAPACK procedure PDGESVD.
Martin Becka - One of the best experts on this subject based on the ideXlab platform.
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PPAM (1) - Parallel One–Sided Jacobi SVD Algorithm with Variable Blocking Factor
Parallel Processing and Applied Mathematics, 2014Co-Authors: Martin Becka, Gabriel OksaAbstract:Parallel one-sided block-Jacobi algorithm for the matrix singular value decomposition (SVD) requires an efficient computation of symmetric Gram matrices, their eigenvalue decompositions (EVDs) and an update of matrix columns and right singular vectors by matrix multiplication. In our recent parallel implementation with \(p\) processors and blocking factor \(\ell =2p\), these tasks are computed serially in each processor in a given parallel Iteration Step because each processor contains exactly two block columns of an input matrix \(A\). However, as shown in our previous work, with increasing \(p\) (hence, with increasing blocking factor) the number of parallel Iteration Steps needed for the convergence of the whole algorithm increases linearly but faster than proportionally to \(p\), so that it is hard to achieve a good speedup. We propose to break the tight relation \(\ell =2p\) and to use a small blocking factor \(\ell = p/k\) for some integer \(k\) that divides \(p\), \(\ell \) even. The algorithm then works with pairs of logical block columns that are distributed among processors so that all computations inside a parallel Iteration Step are themselves parallel. We discuss the optimal data distribution for parallel subproblems in the one-sided block-Jacobi algorithm and analyze its computational and communication complexity. Experimental results with full matrices of order \(8192\) show that our new algorithm with a small blocking factor is well scalable and can be \(2\)–\(3\) times faster than the ScaLAPACK procedure PDGESVD.
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parallel one sided jacobi svd algorithm with variable blocking factor
International Conference on Parallel Processing, 2013Co-Authors: Martin Becka, Gabriel OksaAbstract:Parallel one-sided block-Jacobi algorithm for the matrix singular value decomposition (SVD) requires an efficient computation of symmetric Gram matrices, their eigenvalue decompositions (EVDs) and an update of matrix columns and right singular vectors by matrix multiplication. In our recent parallel implementation with \(p\) processors and blocking factor \(\ell =2p\), these tasks are computed serially in each processor in a given parallel Iteration Step because each processor contains exactly two block columns of an input matrix \(A\). However, as shown in our previous work, with increasing \(p\) (hence, with increasing blocking factor) the number of parallel Iteration Steps needed for the convergence of the whole algorithm increases linearly but faster than proportionally to \(p\), so that it is hard to achieve a good speedup. We propose to break the tight relation \(\ell =2p\) and to use a small blocking factor \(\ell = p/k\) for some integer \(k\) that divides \(p\), \(\ell \) even. The algorithm then works with pairs of logical block columns that are distributed among processors so that all computations inside a parallel Iteration Step are themselves parallel. We discuss the optimal data distribution for parallel subproblems in the one-sided block-Jacobi algorithm and analyze its computational and communication complexity. Experimental results with full matrices of order \(8192\) show that our new algorithm with a small blocking factor is well scalable and can be \(2\)–\(3\) times faster than the ScaLAPACK procedure PDGESVD.
Avi Ostfeld - One of the best experts on this subject based on the ideXlab platform.
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iterative linearization scheme for convex nonlinear equations application to optimal operation of water distribution systems
Journal of Water Resources Planning and Management, 2013Co-Authors: Eyal Price, Avi OstfeldAbstract:Convex equations exist in different fields of research. As an example are the Hazen-Williams or Darcy-Weisbach head-loss formulas and chlorine decay in water supply systems. Pure linear programming (LP) cannot be directly applied to these equations and heuristic techniques must be used. This study presents a methodology for linearization of increasing or decreasing convex nonlinear equations and their incorporation into LP optimization models. The algorithm is demonstrated on the Hazen-Williams head-loss equation combined with a LP optimal operation water supply model. The Hazen-Williams equation is linearized between two points along the nonlinear flow curve. The first point is a fixed point optimally located in the expected flow domain according to maximum flow rate expected in the pipe (estimated through maximum flow velocities and pipe diameter). The second point is the calculated flow rate in the pipe resulting from the previous Iteration Step solution. In each Iteration Step, the linear coefficients are altered according to the previous Step's flow rate result and the fixed point. The solution gradually converges closer to the nonlinear head-loss equation results. The iterative process stops once both an optimal solution is attained and a satisfactory approximation is received. The methodology is demonstrated using simple and complex example applications. DOI: 10.1061/(ASCE)WR.1943-5452.0000275. © 2013 American Society of Civil Engineers. CE Database subject headings: Optimization; Water distribution systems; Chlorine; Water supply. Author keywords: Convex; Optimization; Water distribution systems; Optimal operation; Successive linearization; Head loss.
N. V. Kupryaev - One of the best experts on this subject based on the ideXlab platform.
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Calculation of the Precession of the Perihelion of Mercury’s Orbit Within the Framework of Newton’s Law of Universal Gravitation
Russian Physics Journal, 2015Co-Authors: N. V. KupryaevAbstract:The precession of the perihelion of Mercury’s orbit in the gravitational field of the Sun and planets has been numerically modeled within the framework of Newton’s law of universal gravitation. The calculations were performed with enhanced calculational accuracy and with an Iteration Step of 0.0005 s. It has been shown that the average precession of Mercury’s orbit after 100 years within the framework of Newton’s law of universal gravitation comprises +553''. This is 21'' greater than the generally accepted value of +532''.
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Calculation of the Precession of the Perihelion of Mercury’s Orbit Within the Framework of a Generalized Law of Universal Gravitation
Russian Physics Journal, 2014Co-Authors: N. V. KupryaevAbstract:The precession of the perihelion of Mercury’s orbit in the gravitational field of the Sun and an averaged field of the planets is numerically modeled within the framework of a generalized law of universal gravitation. The calculations were carried out with enhanced calculational accuracy with an Iteration Step of 0.0005 s. It is shown that the average precession of the orbit of Mercury after 100 years within the framework of the given generalization stands at +560''. This is less than the observed shift of the perihelion of Mercury’s orbit by 15'', but greater than the result obtained within the framework of Newton’s classical law of universal gravitation by 28''.
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calculation of the precession of the perihelion of mercury s orbit within the framework of a generalized law of universal gravitation
Russian Physics Journal, 2014Co-Authors: N. V. KupryaevAbstract:The precession of the perihelion of Mercury’s orbit in the gravitational field of the Sun and an averaged field of the planets is numerically modeled within the framework of a generalized law of universal gravitation. The calculations were carried out with enhanced calculational accuracy with an Iteration Step of 0.0005 s. It is shown that the average precession of the orbit of Mercury after 100 years within the framework of the given generalization stands at +560''. This is less than the observed shift of the perihelion of Mercury’s orbit by 15'', but greater than the result obtained within the framework of Newton’s classical law of universal gravitation by 28''.
Feng Zhao - One of the best experts on this subject based on the ideXlab platform.
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optimal selection based suppressed fuzzy c means clustering algorithm with self tuning non local spatial information for image segmentation
Expert Systems With Applications, 2014Co-Authors: Feng ZhaoAbstract:Suppressed fuzzy c-means clustering algorithm (S-FCM) is one of the most effective fuzzy clustering algorithms. Even if S-FCM has some advantages, some problems exist. First, it is unreasonable to compulsively modify the membership degree values for all the data points in each Iteration Step of S-FCM. Furthermore, duo to only utilizing the spatial information derived from the pixel's neighborhood window to guide the process of image segmentation, S-FCM cannot obtain satisfactory segmentation results on images heavily corrupted by noise. This paper proposes an optimal-selection-based suppressed fuzzy c-means clustering algorithm with self-tuning non local spatial information for image segmentation to solve the above drawbacks of S-FCM. Firstly, an optimal-selection-based suppressed strategy is presented to modify the membership degree values for data points. In detail, during each Iteration Step, all the data points are ranked based on their biggest membership degree values, and then the membership degree values of the top r ranked data points are modified while the membership degree values of the other data points are not changed. In this paper, the parameter r is determined by the golden section method. Secondly, a novel gray level histogram is constructed by using the self-tuning non local spatial information for each pixel, and then fuzzy c-means clustering algorithm with the optimal-selection-based suppressed strategy is executed on this histogram. The self-tuning non local spatial information of a pixel is derived from the pixels with a similar neighborhood configuration to the given pixel and can preserve more information of the image than the spatial information derived from the pixel's neighborhood window. This method is applied to Berkeley and other real images heavily contaminated by noise. The image segmentation experiments demonstrate the superiority of the proposed method over other fuzzy algorithms.
