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August 2017 - Volume 6, Number 2/3

SVD BASED LATENT SEMANTIC INDEXING WITH USE OF THE GPU COMPUTATIONS

Raczynski Damian and Stanisławski Wlodzimierz, University of Applied Science in Nysa, Poland
 

Abstract: The purpose of this article is to determine the usefulness of the Graphics Processing Unit (GPU) calculations used to implement the Latent Semantic Indexing (LSI) reduction of the TERM-BY-DOCUMENT matrix. Considered reduction of the matrix is based on the use of the SVD (Singular Value Decomposition) decomposition. A high computational complexity of the SVD decomposition - O(n3), causes that a reduction of a large indexing structure is a difficult task. In this article there is a comparison of the time complexity and accuracy of the algorithms implemented for two different environments. The first environment is associated with the CPU and MATLAB R2011a. The second environment is related to graphics processors and the CULA library. The calculations were carried out on generally available benchmark matrices, which were combined to achieve the resulting matrix of high size. For both considered environments computations were performed for double and single precision data.

 
Keywords: LSI, GPU, reduction, parallel computing, SVD
 
  

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A CLASS OF BOUNDARY VALUE METHODS FOR THE COMPLEX DELAY DIFFERENTIAL EQUATION

Shifeng Wu, Guangdong Polytechnic Normal University, China
 

Abstract: In this paper, a class of boundary value methods (BVMs) for delay differential equations (DDEs) is considered. The delay dependent stable regions of the extended trapezoidal rules of second kind (ETR2s), which are a class of BVMs, are displayed for the test equation of DDEs. Furthermore, it is showed ETR2s cannot preserve the delay-dependent stability of the complex coefficient test equation considered. Some numerical experiments are given to confirm the theoretical results. AMS 2000 Mathematics Subject Classification: 65L20, 65M12

 
Keywords: Delay differential equations; boundary value methods; delay-dependent stability; extended trapezoidal rules of second kind
 
  

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February 2017 - Volume 6, Number 1

A NEW APPROACH TO M(G)-GROUP SOFT UNION ACTION AND ITS APPLICATIONS TO M(G)-GROUP THEORY

P. Jeyaraman1 and R. Nagarajan2, 1Bharathiar University, India and 2J J College of Engineering & Technology, India
 

Abstract: In this paper, we define a new type of M(G)-group action , called M(G)-group soft union(SU) action and M(G)-ideal soft union(SU) action on a soft set. This new concept illustrates how a soft set effects on an M(G)-group in the mean of union and inclusion of sets and its function as bridge among soft set theory, set theory and M(G)-group theory. We also obtain some analog of classical M(G)- group theoretic concepts for M(G)-group SU-action. Finally, we give the application of SU-actions on M(G)-group to M(G)-group theory..

 
Keywords: soft set, M(G)-group, M(G)-group SU-action, M(G)--ideal SU-action, soft pre-image, soft anti-image, α-inclusion.
 
  

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