The Experts below are selected from a list of 1491 Experts worldwide ranked by ideXlab platform
Yong Zhang - One of the best experts on this subject based on the ideXlab platform.
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flexible Incomplete Cholesky factorization with multi parameters to control the number of nonzero elements in preconditioners
Numerical Linear Algebra With Applications, 2012Co-Authors: Yong Zhang, Tingzhu Huang, Yanfei JingAbstract:An Incomplete Cholesky (IC) factorization with multi-parameters is presented. The marked virtue of the proposed IC factorization algorithm is to dynamically control the number of nonzero elements in each column of the IC factorization preconditioner L with the help of these involved parameters. Parameter setting strategies are also given. Numerical results show that the total computing time for both computation of the preconditioner L and iterative solution is evidently reduced for almost all test matrices. In general, these parameters can obviously enhance the effectiveness and performance of the IC factorization. Copyright 2011 John Wiley & Sons, Ltd.
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application of the Incomplete Cholesky factorization preconditioned krylov subspace method to the vector finite element method for 3 d electromagnetic scattering problems
Computer Physics Communications, 2010Co-Authors: Tingzhu Huang, Yanfei Jing, Yong ZhangAbstract:The Incomplete Cholesky (IC) factorization preconditioning technique is applied to the Krylov subspace methods for solving large systems of linear equations resulted from the use of edge-based finite element method (FEM). The construction of the preconditioner is based on the fact that the coefficient matrix is represented in an upper triangular compressed sparse row (CSR) form. An efficient implementation of the IC factorization is described in detail for complex symmetric matrices. With some ordering schemes our IC algorithm can greatly reduce the memory requirement as well as the iteration numbers. Numerical tests on harmonic analysis for plane wave scattering from a metallic plate and a metallic sphere coated by a lossy dielectric layer show the efficiency of this method.
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MODIFIED Incomplete Cholesky FACTORIZATION FOR SOLVING ELECTROMAGNETIC SCATTERING PROBLEMS
Progress In Electromagnetics Research B, 2009Co-Authors: Tingzhu Huang, Yong Zhang, Wei Shao, Sheng-jian LaiAbstract:In this paper, we study a class of modified Incomplete Cholesky factorization preconditioners LLT with two control parameters including dropping rules. Before computing preconditioners, the modified Incomplete Cholesky factorization algorithm allows to decide the sparsity of Incomplete factorization preconditioners by two fillin control parameters: (1) p, the number of the largest number p of nonzero entries in each row; (2) dropping tolerance. With RCM reordering scheme as a crucial operation for Incomplete factorization preconditioners, our numerical results show that both the number of PCOCG and PCG iterations and the total computing time are reduced evidently for appropriate fill-in control parameters. Numerical tests on harmonic analysis for 2D and 3D scattering problems show the efficiency of our method.
Tingzhu Huang - One of the best experts on this subject based on the ideXlab platform.
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flexible Incomplete Cholesky factorization with multi parameters to control the number of nonzero elements in preconditioners
Numerical Linear Algebra With Applications, 2012Co-Authors: Yong Zhang, Tingzhu Huang, Yanfei JingAbstract:An Incomplete Cholesky (IC) factorization with multi-parameters is presented. The marked virtue of the proposed IC factorization algorithm is to dynamically control the number of nonzero elements in each column of the IC factorization preconditioner L with the help of these involved parameters. Parameter setting strategies are also given. Numerical results show that the total computing time for both computation of the preconditioner L and iterative solution is evidently reduced for almost all test matrices. In general, these parameters can obviously enhance the effectiveness and performance of the IC factorization. Copyright 2011 John Wiley & Sons, Ltd.
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application of the Incomplete Cholesky factorization preconditioned krylov subspace method to the vector finite element method for 3 d electromagnetic scattering problems
Computer Physics Communications, 2010Co-Authors: Tingzhu Huang, Yanfei Jing, Yong ZhangAbstract:The Incomplete Cholesky (IC) factorization preconditioning technique is applied to the Krylov subspace methods for solving large systems of linear equations resulted from the use of edge-based finite element method (FEM). The construction of the preconditioner is based on the fact that the coefficient matrix is represented in an upper triangular compressed sparse row (CSR) form. An efficient implementation of the IC factorization is described in detail for complex symmetric matrices. With some ordering schemes our IC algorithm can greatly reduce the memory requirement as well as the iteration numbers. Numerical tests on harmonic analysis for plane wave scattering from a metallic plate and a metallic sphere coated by a lossy dielectric layer show the efficiency of this method.
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MODIFIED Incomplete Cholesky FACTORIZATION FOR SOLVING ELECTROMAGNETIC SCATTERING PROBLEMS
Progress In Electromagnetics Research B, 2009Co-Authors: Tingzhu Huang, Yong Zhang, Wei Shao, Sheng-jian LaiAbstract:In this paper, we study a class of modified Incomplete Cholesky factorization preconditioners LLT with two control parameters including dropping rules. Before computing preconditioners, the modified Incomplete Cholesky factorization algorithm allows to decide the sparsity of Incomplete factorization preconditioners by two fillin control parameters: (1) p, the number of the largest number p of nonzero entries in each row; (2) dropping tolerance. With RCM reordering scheme as a crucial operation for Incomplete factorization preconditioners, our numerical results show that both the number of PCOCG and PCG iterations and the total computing time are reduced evidently for appropriate fill-in control parameters. Numerical tests on harmonic analysis for 2D and 3D scattering problems show the efficiency of our method.
Charlie Chungping Chen - One of the best experts on this subject based on the ideXlab platform.
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efficient large scale power grid analysis based on preconditioned krylov subspace iterative methods
Design Automation Conference, 2001Co-Authors: Tsunghao Chen, Charlie Chungping ChenAbstract:In this paper, we propose preconditioned Krylov-subspace iterative methods to perform efficient DC and transient simulations for large-scale linear circuits with an emphasis on power delivery circuits. We also prove that a circuit with inductors can be simplified from MNA to NA format, and the matrix becomes an s.p.d matrix. This property makes it suitable for the conjugate gradient with Incomplete Cholesky decomposition as the preconditioner , which is faster than other direct and iterative methods. Extensive experimental results on large-scale industrial power grid circuits show that our method is over 200 times faster for DC analysis and around 10 times faster for transient simulation compared to SPICE3. Furthermore, our algorithm reduces over 75% of memory usage than SPICE3 while the accuracy is not compromised.
Mx Y - One of the best experts on this subject based on the ideXlab platform.
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CHARACTER*1 CHECK 3 Description
2013Co-Authors: Mx YAbstract:Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose F11JBF solves a system of linear equations involving the Incomplete Cholesky preconditioning matrix generated by F11JAF
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CHARACTER*1 CHECK 3 Description
2013Co-Authors: Mx YAbstract:Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose F11JPF solves a system of complex linear equations involving the Incomplete Cholesky preconditioning matrix generated by F11JNF
Johan A K Suykens - One of the best experts on this subject based on the ideXlab platform.
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entropy based Incomplete Cholesky decomposition for a scalable spectral clustering algorithm computational studies and sensitivity analysis
Entropy, 2016Co-Authors: Rocco Langone, Marc Van Barel, Johan A K SuykensAbstract:Spectral clustering methods allow datasets to be partitioned into clusters by mapping the input datapoints into the space spanned by the eigenvectors of the Laplacian matrix. In this article, we make use of the Incomplete Cholesky decomposition (ICD) to construct an approximation of the graph Laplacian and reduce the size of the related eigenvalue problem from N to m, with m ≪ N. In particular, we introduce a new stopping criterion based on normalized mutual information between consecutive partitions, which terminates the ICD when the change in the cluster assignments is below a given threshold. Compared with existing ICD-based spectral clustering approaches, the proposed method allows the reduction of the number m of selected pivots (i.e., to obtain a sparser model) and at the same time, to maintain high clustering quality. The method scales linearly with respect to the number of input datapoints N and has low memory requirements, because only matrices of size N × m and m × m are calculated (in contrast to standard spectral clustering, where the construction of the full N × N similarity matrix is needed). Furthermore, we show that the number of clusters can be reliably selected based on the gap heuristics computed using just a small matrix R of size m × m instead of the entire graph Laplacian. The effectiveness of the proposed algorithm is tested on several datasets.
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sparse kernel models for spectral clustering using the Incomplete Cholesky decomposition
International Joint Conference on Neural Network, 2008Co-Authors: Carlos Alzate, Johan A K SuykensAbstract:A new sparse kernel model for spectral clustering is presented. This method is based on the Incomplete Cholesky decomposition and can be used to efficiently solve large-scale spectral clustering problems. The formulation arises from a weighted kernel principal component analysis (PCA) interpretation of spectral clustering. The interpretation is within a constrained optimization framework with primal and dual model representations allowing the clustering model to be extended to out-of-sample points. The Incomplete Cholesky decomposition is used to compute low-rank approximations of a modified affinity matrix derived from the data which contains cluster information. A reduced set method is also presented to compute efficiently the cluster indicators for out-of-sample data. Simulation results with large-scale toy datasets and images show improved performance in terms of computational complexity.
