• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.351-361
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• 2010

The solution of large sparse linear systems is one of the most important problems in large scale scientific computing. Among the many methods developed, the preconditioned Krylov subspace methods are considered the preferred methods. Selecting a suitable preconditioner with appropriate parameters for a specific sparse linear system presents a challenging task for many application scientists and engineers who have little knowledge of preconditioned iterative methods. The prediction of ILU type preconditioners was considered in [27] where support vector machine(SVM), as a data mining technique, is used to classify large sparse linear systems and predict best preconditioners. In this paper, we apply the data mining approach to the sparse approximate inverse(SAI) type preconditioners to find some parameters with which the preconditioned Krylov subspace method on the linear systems shows best performance.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.147-159
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• 1997

It is important to solve the large sparse linear system appeared in many application field such as $AA^Ty={\beta}$ efficiently. In solving this linear system, the sparse solver using the splitting method for the relatively dense column is experimentally better than the direct solver using the Cholesky method.

• 전기의세계
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• v.23 no.3
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• pp.43-52
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• 1974

The matrix inversion is very inefficient for computing direct solutions of the large spare systems of linear equations that arise in many network problems as a large electrical power system. Optimally ordered triangular factorization of sparse matrices is more efficient and offers the other important computational advantages in some applications with this method. The direct solutions are computed from sparse matrix factors instead of a full inverse matrix, thereby gaining a significant advantage is speed and computer memory requirements. In this paper, it is shown that the sparse matrix method is superior to the inverse matrix method to solve the linear equations of large sparse networks. In addition, it is shown that the sparse matrix method is superior to the inverse matrix method to solve the linear equations of large sparse networks. In addition, it is shown that the solutions may be applied directly to sove the load flow in an electrical power system. The result of this study should lead to many aplications including short circuit, transient stability, network reduction, reactive optimization and others.

• The KIPS Transactions:PartA
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• v.8A no.3
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• pp.227-234
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• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditiner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to $1025{\times}1024$. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications, The results show that Multi-Color Block SOR is scalabl and gives the best performances.

• Journal of the Korean Institute of Telematics and Electronics
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• v.11 no.2
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• pp.1-4
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• 1974

Matrix inversion is very inefficient for computing direct solutions of the large sparse systems of linear equations that arise in many network problems. This paper describes some computer programming techniques for taking advantage of the sparsity of the admittance matrix. with this method, direct solutions are computed from sparse matrix. It is Possible to gain a significant reduction in computing time, memory and round-off emir[r. Retails of the method, numerical examples and programming are given.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.7
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• pp.3594-3607
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• 2017

The traditional feature extraction methods such as principal component analysis (PCA) cannot obtain the local structure of the samples, and locally linear embedding (LLE) cannot obtain the global structure of the samples. However, a common drawback of existing PCA and LLE algorithm is that they cannot deal well with the sparse problem of the samples. Therefore, by integrating the globality of PCA and the locality of LLE with a sparse constraint, we developed an improved and unsupervised difference algorithm called Sparse Difference Embedding (SDE), for dimensionality reduction of high-dimensional data in small sample size problems. Significantly differing from the existing PCA and LLE algorithms, SDE seeks to find a set of perfect projections that can not only impact the locality of intraclass and maximize the globality of interclass, but can also simultaneously use the Lasso regression to obtain a sparse transformation matrix. This characteristic makes SDE more intuitive and more powerful than PCA and LLE. At last, the proposed algorithm was estimated through experiments using the Yale and AR face image databases and the USPS handwriting digital databases. The experimental results show that SDE outperforms PCA LLE and UDP attributed to its sparse discriminating characteristics, which also indicates that the SDE is an effective method for face recognition.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.283-296
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• 2005

It is well known that the ordering of the unknowns can have a significant effect on the convergence of a preconditioned iterative method and on its implementation on a parallel computer. To do so, we introduce a block red-black coloring to increase the degree of parallelism in the application of the block ILU preconditioner for solving sparse matrices, arising from convection-diffusion equations discretized using the finite difference scheme (five-point operator). We study the preconditioned PGMRES iterative method for solving these linear systems.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.14 no.4
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• pp.388-397
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• 1989

This paper describes an intelligent iterative parallel algorithm for solving large sparse linear systems of equations, and proposes a ststic dataflow computer architechture for the implementation of the algorithm. Implemented with the Jacobi interative method, the intelligent algorithm reduces the parallel execution time by reducing the individual inner product operation time.

• The KIPS Transactions:PartA
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• v.8A no.4
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• pp.439-446
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• 2001

The main stream of parallel programming today is using synchronous algorithms, where processor synchronization for correct computation and workload balance are essential. Overall performance of the whole system is dependent upon the performance of the slowest processor, if workload is not well-balanced or heterogeneous clusters are used. Asynchronous iteration is a way to mitigate such problems, but most of the works done so far are for shared memory systems. In this paper, we suggest and implement a parallel large sparse linear system solver that improves performance on distributed memory systems like clusters by reducing processor idle times as much as possible by asynchronous iterations.

• Journal of the Korea Society of Computer and Information
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• v.26 no.1
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• pp.1-9
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• 2021

OpenGL compute shader is a shader stage that operate differently from other shader stage and it can be used for the calculating purpose of any data in parallel. This paper proposes a GPU-based parallel algorithm for computing sparse linear systems through conjugate gradient using an iterative method, which perform calculation on OpenGL compute shader. Basically, this sparse linear solver is used to solve large linear systems such as symmetric positive definite matrix. Four well-known matrix formats (Dense, COO, ELL and CSR) have been used for matrix storage. The performance comparison from our experimental tests using eight sparse matrices shows that GPU-based linear solving system much faster than CPU-based linear solving system with the best average computing time 0.64ms in GPU-based and 15.37ms in CPU-based.