Factorization Process

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Klaus Gartner - One of the best experts on this subject based on the ideXlab platform.

  • solving unsymmetric sparse systems of linear equations with pardiso
    Future Generation Computer Systems, 2004
    Co-Authors: Olaf Schenk, Klaus Gartner
    Abstract:

    Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU Factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and unsymmetric prepermutation of rows is used to place large matrix entries on the diagonal. Complete block diagonal supernode pivoting allows dynamical interchanges of columns and rows during the Factorization Process. The level-3 BLAS efficiency is retained and an advanced two-level left-right looking scheduling scheme results in good speedup on SMP machines. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications.

  • solving unsymmetric sparse systems of linear equations with pardiso
    International Conference on Computational Science, 2002
    Co-Authors: Olaf Schenk, Klaus Gartner
    Abstract:

    Supernode pivoting for unsymmetric matrices coupled with supernode partitioning and asynchronous computation can achieve high gigaflop rates for parallel sparse LU Factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and prepermutation of rows is used to place large matrix entries on the diagonal. Supernode pivoting allows dynamical interchanges of columns and rows during the Factorization Process. The BLAS-3 level efficiency is retained. An enhanced left-right looking scheduling scheme is uneffected and results in good speedup on SMP machines without increasing the operation count. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications.

  • International Conference on Computational Science (2) - Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO
    Lecture Notes in Computer Science, 2002
    Co-Authors: Olaf Schenk, Klaus Gartner
    Abstract:

    Supernode pivoting for unsymmetric matrices coupled with supernode partitioning and asynchronous computation can achieve high gigaflop rates for parallel sparse LU Factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and prepermutation of rows is used to place large matrix entries on the diagonal. Supernode pivoting allows dynamical interchanges of columns and rows during the Factorization Process. The BLAS-3 level efficiency is retained. An enhanced left-right looking scheduling scheme is uneffected and results in good speedup on SMP machines without increasing the operation count. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications.

Olaf Schenk - One of the best experts on this subject based on the ideXlab platform.

  • solving unsymmetric sparse systems of linear equations with pardiso
    Future Generation Computer Systems, 2004
    Co-Authors: Olaf Schenk, Klaus Gartner
    Abstract:

    Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU Factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and unsymmetric prepermutation of rows is used to place large matrix entries on the diagonal. Complete block diagonal supernode pivoting allows dynamical interchanges of columns and rows during the Factorization Process. The level-3 BLAS efficiency is retained and an advanced two-level left-right looking scheduling scheme results in good speedup on SMP machines. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications.

  • solving unsymmetric sparse systems of linear equations with pardiso
    International Conference on Computational Science, 2002
    Co-Authors: Olaf Schenk, Klaus Gartner
    Abstract:

    Supernode pivoting for unsymmetric matrices coupled with supernode partitioning and asynchronous computation can achieve high gigaflop rates for parallel sparse LU Factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and prepermutation of rows is used to place large matrix entries on the diagonal. Supernode pivoting allows dynamical interchanges of columns and rows during the Factorization Process. The BLAS-3 level efficiency is retained. An enhanced left-right looking scheduling scheme is uneffected and results in good speedup on SMP machines without increasing the operation count. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications.

  • International Conference on Computational Science (2) - Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO
    Lecture Notes in Computer Science, 2002
    Co-Authors: Olaf Schenk, Klaus Gartner
    Abstract:

    Supernode pivoting for unsymmetric matrices coupled with supernode partitioning and asynchronous computation can achieve high gigaflop rates for parallel sparse LU Factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and prepermutation of rows is used to place large matrix entries on the diagonal. Supernode pivoting allows dynamical interchanges of columns and rows during the Factorization Process. The BLAS-3 level efficiency is retained. An enhanced left-right looking scheduling scheme is uneffected and results in good speedup on SMP machines without increasing the operation count. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications.

Bin Gao - One of the best experts on this subject based on the ideXlab platform.

  • single channel informed signal separation using artificial stereophonic mixtures and exemplar guided matrix factor deconvolution
    International Journal of Adaptive Control and Signal Processing, 2018
    Co-Authors: Ahmed Altmeme, Wai Lok Woo, S S Dlay, Bin Gao
    Abstract:

    In this paper, a method is proposed to tackle the problem of single channel audio separation. The proposed method leverages on the exemplar source is used to emulate the targeted speech signal. A multicomponent nonnegative matrix factor 2D deconvolution (NMF2D) is proposed to model the temporal and spectral changes and the number of spectral basis of the audio signals. The paper proposes an artificial auxiliary channel to imitate a pair of stereo mixture signals, which is termed as “artificial-stereophonic mixtures.” The artificial-stereophonic mixtures and the exemplar source are jointly used to guide the Factorization Process of the NMF2D. The Factorization is adapted under a hybrid framework that combines the generalized expectation–maximization algorithm with multiplicative update adaptation. The proposed algorithm leads to fast and stable convergence and ensures the nonnegativity constraints of the solution are satisfied. Adaptive sparsity has also been introduced on each sparse parameter in the multicomponent NMF2D model when the exemplar deviates from the target signal. Experimental results have shown the competence of the proposed algorithms in comparison with other algorithms.

  • Single channel informed signal separation using artificial‐stereophonic mixtures and exemplar‐guided matrix factor deconvolution
    International Journal of Adaptive Control and Signal Processing, 2018
    Co-Authors: Ahmed Al-tmeme, Wai Lok Woo, S S Dlay, Bin Gao
    Abstract:

    In this paper, a method is proposed to tackle the problem of single channel audio separation. The proposed method leverages on the exemplar source is used to emulate the targeted speech signal. A multicomponent nonnegative matrix factor 2D deconvolution (NMF2D) is proposed to model the temporal and spectral changes and the number of spectral basis of the audio signals. The paper proposes an artificial auxiliary channel to imitate a pair of stereo mixture signals, which is termed as “artificial-stereophonic mixtures.” The artificial-stereophonic mixtures and the exemplar source are jointly used to guide the Factorization Process of the NMF2D. The Factorization is adapted under a hybrid framework that combines the generalized expectation–maximization algorithm with multiplicative update adaptation. The proposed algorithm leads to fast and stable convergence and ensures the nonnegativity constraints of the solution are satisfied. Adaptive sparsity has also been introduced on each sparse parameter in the multicomponent NMF2D model when the exemplar deviates from the target signal. Experimental results have shown the competence of the proposed algorithms in comparison with other algorithms.

Robert A. Van De Geijn - One of the best experts on this subject based on the ideXlab platform.

  • Sparse direct Factorizations through unassembled hyper-matrices
    Computer Methods in Applied Mechanics and Engineering, 2010
    Co-Authors: Paolo Bientinesi, Victor Eijkhout, Kyungjoo Kim, Jason Kurtz, Robert A. Van De Geijn
    Abstract:

    Abstract We present a novel strategy for sparse direct Factorizations that is geared towards the matrices that arise from hp -adaptive Finite Element Methods. In that context, a sequence of linear systems derived by successive local refinement of the problem domain needs to be solved. Thus, there is an opportunity for a Factorization strategy that proceeds by updating (and possibly downdating) the Factorization. Our scheme consists of storing the matrix as unassembled element matrices, hierarchically ordered to mirror the refinement history of the domain. The Factorization of such an ‘unassembled hyper-matrix’ proceeds in terms of element matrices, only assembling nodes when they need to be eliminated. The main benefits are efficiency from the fact that only updates to the Factorization are made, high scalar efficiency since the Factorization Process uses dense matrices throughout, and a workflow that integrates naturally with the application.

Hae-won Park - One of the best experts on this subject based on the ideXlab platform.

  • qpSWIFT: A Real-Time Sparse Quadratic Program Solver for Robotic Applications
    IEEE Robotics and Automation Letters, 2019
    Co-Authors: Abhishek Pandala, Yanran Ding, Hae-won Park
    Abstract:

    In this letter, we present qpSWIFT, a real-time quadratic program (QP) solver. Motivated by the need for a robust embedded QP solver in robotic applications, qpSWIFT employs standard primal-dual interior-point method, along with Mehrotra predictor–corrector steps and Nesterov–Todd scaling. The sparse structure of the resulting Karush–Kuhn–Tucker linear system in the QP formulation is exploited, and sparse direct methods are utilized to solve the linear system of equations. To further accelerate the Factorization Process, we only modify the corresponding rows of the matrix factors that change during iterations and cache the nonzero Cholesky pattern. qpSWIFT is library free, written in ANSI-C and its performance is benchmarked through standard problems that could be cast as QP. Numerical results show that qpSWIFT outperforms state-of-the-art solvers for small scale problems. To evaluate the performance of the solver, a real-time implementation of the solver in the model predictive control framework through experiments on a quadrupedal robot are presented.