Upper Triangular Form

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Jack Dongarra - One of the best experts on this subject based on the ideXlab platform.

  • soft error resilient qr factorization for hybrid system with gpgpu
    Journal of Computational Science, 2013
    Co-Authors: Piotr Luszczek, Jack Dongarra, Stanimire Tomov
    Abstract:

    Abstract The general purpose graphics processing units (GPGPUs) are increasingly deployed for scientific computing due to their perFormance advantages over CPUs. What followed is the fact that fault tolerance has become a more serious concern compared to the period when GPGPUs were used exclusively for graphics applications. Using GPUs and CPUs together in a hybrid computing system increases flexibility and perFormance but also increases the possibility of the computations being affected by soft errors, for example, in the Form of bit flips. In this work, we propose a soft error resilient algorithm for QR factorization on such hybrid systems. Our contributions include: (1) a checkpointing and recovery mechanism for the left-factor Q whose perFormance is scalable on hybrid systems; (2) optimized Givens rotation utilities on GPGPUs to efficiently reduce an Upper Hessenberg matrix to an Upper Triangular Form for the protection of the right factor R ; and (3) a recovery algorithm based on QR update on GPGPUs. Experimental results show that our fault tolerant QR factorization can successfully detect and recover from soft errors in the entire matrix with little overhead on hybrid systems with GPGPUs.

  • soft error resilient qr factorization for hybrid system with gpgpu
    Proceedings of the second workshop on Scalable algorithms for large-scale systems, 2011
    Co-Authors: Piotr Luszczek, Stanimire Tomov, Jack Dongarra
    Abstract:

    The general purpose graphics processing units (GPGPU) are increasingly deployed for scientific computing due to their perFormance advantages over CPUs. As a result, fault tolerance has become a more serious concern compared to the period when GPGPUs were used exclusively for graphics applications. Using GPUs and CPUs together in a hybrid computing system increases flexibility and perFormance but also increases the possibility of the computations being affected by soft errors. In this work, we propose a soft error resilient algorithm for QR factorization on such hybrid systems. Our contributions include (1) a checkpointing and recovery mechanism for the left-factor Q whose perFormance is scalable on hybrid systems; (2) optimized Givens rotation utilities on GPGPUs to efficiently reduce an Upper Hessenberg matrix to an Upper Triangular Form for the protection of the right factor R, and (3) a recovery algorithm based on QR update on GPGPUs. Experimental results show that our fault tolerant QR factorization can success- fully detect and recover from soft errors in the entire matrix with little overhead on hybrid systems with GPGPUs.

  • soft error resilient qr factorization for hybrid system
    University of Tennessee Computer Science Technical Report, 2011
    Co-Authors: Piotr Luszczek, Stanimire Tomov, Jack Dongarra
    Abstract:

    As the general purpose graphics processing units (GPGPU) are increasingly deployed for scientific computing for its raw perFormance advantages compared to CPUs, the fault tolerance issue has started to become more of a concern than before when they were exclusively used for graphics applications. The pairing of GPUs with CPUs to Form a hybrid computing systems for better flexibility and perFormance creates a massive amounts of computations that have a higher possibility to be affected by transient error – a soft error that silently modifies data causing errors to pass unnoticed. This is despite the fact that the newest Fermi generation of GPUs from NVIDIA are equipped with error correcting units to protect their memories. This problem is particularly serious for applications that employ numerical linear algebra since large sections of data are often modified between steps, and therefore even a single error could eventually propagate into a large area of result. In order to give protection to dense linear algebra computations on such hybrid systems, we developed an algorithm that is resilient to soft errors. We chose the right-looking Householder QR factorization as a demonstration of our algorithm for a hybrid system that features both GPUs and CPUs. Algorithm based fault tolerance (ABFT) is used to protect from errors in the trailing matrix and the right factor, while a checkpointing method is used to ensure the left factor is error-free. This work is based on a previous study of fault tolerance in matrix factorizations. Our contribution includes (1) a stable multiple-error checkpointing and recovery mechanism for the left-factor, which is also scalable in perFormance in the hybrid execution environment and does not cause severe perFormance degradation. (2) optimized Givens rotation utilities on the GPU to efficiently reduce an Upper Hessenberg matrix to Upper Triangular Form, and (3) a recovery algorithm based on QR update inside a hybrid system. Experimental results show that, our fault tolerant QR factorization can successfully detect and correct data altered by soft errors in both the left and right factors and we observe a decreasing percentage of overhead as the matrix size grows.

Ming Cao - One of the best experts on this subject based on the ideXlab platform.

  • distributed global output feedback control for a class of euler lagrange systems
    arxiv:eess.SY, 2019
    Co-Authors: Qingkai Yang, Hao Fang, Jie Chen, Zhongping Jiang, Ming Cao
    Abstract:

    This published paper investigates the distributed tracking control problem for a class of Euler-Lagrange multi-agent systems when the agents can only measure the positions. In this case, the lack of the separation principle and the strong nonlinearity in unmeasurable states pose severe technical challenges to global output-feedback control design. To overcome these difficulties, a global nonsingular coordinate transFormation matrix in the Upper Triangular Form is firstly proposed such that the nonlinear dynamic model can be partially linearized with respect to the unmeasurable states. And, a new type of velocity observers is designed to estimate the unmeasurable velocities for each system. Then, based on the outputs of the velocity observers, we propose distributed control laws that enable the coordinated tracking control system to achieve uniForm global exponential stability (UGES). Both theoretical analysis and numerical simulations are presented to validate the effectiveness of the proposed control scheme. Followed by the original paper, a typo and a mistake is corrected.

  • distributed global output feedback control for a class of euler lagrange systems
    IEEE Transactions on Automatic Control, 2017
    Co-Authors: Qingkai Yang, Hao Fang, Jie Chen, Zhongping Jiang, Ming Cao
    Abstract:

    This paper investigates the distributed tracking control problem for a class of Euler–Lagrange multiagent systems when the agents can only measure the positions. In this case, the lack of the separation principle and the strong nonlinearity in unmeasurable states pose severe technical challenges to global output-feedback control design. To overcome these difficulties, a global nonsingular coordinate transFormation matrix in the Upper Triangular Form is first proposed such that the nonlinear dynamic model can be partially linearized with respect to the unmeasurable states. And, a new type of velocity observers is designed to estimate the unmeasurable velocities for each system. Then, based on the outputs of the velocity observers, we propose distributed control laws that enable the coordinated tracking control system to achieve uniForm global exponential stability. Both theoretical analysis and numerical simulations are presented to validate the effectiveness of the proposed control scheme.

Piotr Luszczek - One of the best experts on this subject based on the ideXlab platform.

  • soft error resilient qr factorization for hybrid system with gpgpu
    Journal of Computational Science, 2013
    Co-Authors: Piotr Luszczek, Jack Dongarra, Stanimire Tomov
    Abstract:

    Abstract The general purpose graphics processing units (GPGPUs) are increasingly deployed for scientific computing due to their perFormance advantages over CPUs. What followed is the fact that fault tolerance has become a more serious concern compared to the period when GPGPUs were used exclusively for graphics applications. Using GPUs and CPUs together in a hybrid computing system increases flexibility and perFormance but also increases the possibility of the computations being affected by soft errors, for example, in the Form of bit flips. In this work, we propose a soft error resilient algorithm for QR factorization on such hybrid systems. Our contributions include: (1) a checkpointing and recovery mechanism for the left-factor Q whose perFormance is scalable on hybrid systems; (2) optimized Givens rotation utilities on GPGPUs to efficiently reduce an Upper Hessenberg matrix to an Upper Triangular Form for the protection of the right factor R ; and (3) a recovery algorithm based on QR update on GPGPUs. Experimental results show that our fault tolerant QR factorization can successfully detect and recover from soft errors in the entire matrix with little overhead on hybrid systems with GPGPUs.

  • soft error resilient qr factorization for hybrid system with gpgpu
    Proceedings of the second workshop on Scalable algorithms for large-scale systems, 2011
    Co-Authors: Piotr Luszczek, Stanimire Tomov, Jack Dongarra
    Abstract:

    The general purpose graphics processing units (GPGPU) are increasingly deployed for scientific computing due to their perFormance advantages over CPUs. As a result, fault tolerance has become a more serious concern compared to the period when GPGPUs were used exclusively for graphics applications. Using GPUs and CPUs together in a hybrid computing system increases flexibility and perFormance but also increases the possibility of the computations being affected by soft errors. In this work, we propose a soft error resilient algorithm for QR factorization on such hybrid systems. Our contributions include (1) a checkpointing and recovery mechanism for the left-factor Q whose perFormance is scalable on hybrid systems; (2) optimized Givens rotation utilities on GPGPUs to efficiently reduce an Upper Hessenberg matrix to an Upper Triangular Form for the protection of the right factor R, and (3) a recovery algorithm based on QR update on GPGPUs. Experimental results show that our fault tolerant QR factorization can success- fully detect and recover from soft errors in the entire matrix with little overhead on hybrid systems with GPGPUs.

  • soft error resilient qr factorization for hybrid system
    University of Tennessee Computer Science Technical Report, 2011
    Co-Authors: Piotr Luszczek, Stanimire Tomov, Jack Dongarra
    Abstract:

    As the general purpose graphics processing units (GPGPU) are increasingly deployed for scientific computing for its raw perFormance advantages compared to CPUs, the fault tolerance issue has started to become more of a concern than before when they were exclusively used for graphics applications. The pairing of GPUs with CPUs to Form a hybrid computing systems for better flexibility and perFormance creates a massive amounts of computations that have a higher possibility to be affected by transient error – a soft error that silently modifies data causing errors to pass unnoticed. This is despite the fact that the newest Fermi generation of GPUs from NVIDIA are equipped with error correcting units to protect their memories. This problem is particularly serious for applications that employ numerical linear algebra since large sections of data are often modified between steps, and therefore even a single error could eventually propagate into a large area of result. In order to give protection to dense linear algebra computations on such hybrid systems, we developed an algorithm that is resilient to soft errors. We chose the right-looking Householder QR factorization as a demonstration of our algorithm for a hybrid system that features both GPUs and CPUs. Algorithm based fault tolerance (ABFT) is used to protect from errors in the trailing matrix and the right factor, while a checkpointing method is used to ensure the left factor is error-free. This work is based on a previous study of fault tolerance in matrix factorizations. Our contribution includes (1) a stable multiple-error checkpointing and recovery mechanism for the left-factor, which is also scalable in perFormance in the hybrid execution environment and does not cause severe perFormance degradation. (2) optimized Givens rotation utilities on the GPU to efficiently reduce an Upper Hessenberg matrix to Upper Triangular Form, and (3) a recovery algorithm based on QR update inside a hybrid system. Experimental results show that, our fault tolerant QR factorization can successfully detect and correct data altered by soft errors in both the left and right factors and we observe a decreasing percentage of overhead as the matrix size grows.

Qingkai Yang - One of the best experts on this subject based on the ideXlab platform.

  • distributed global output feedback control for a class of euler lagrange systems
    arxiv:eess.SY, 2019
    Co-Authors: Qingkai Yang, Hao Fang, Jie Chen, Zhongping Jiang, Ming Cao
    Abstract:

    This published paper investigates the distributed tracking control problem for a class of Euler-Lagrange multi-agent systems when the agents can only measure the positions. In this case, the lack of the separation principle and the strong nonlinearity in unmeasurable states pose severe technical challenges to global output-feedback control design. To overcome these difficulties, a global nonsingular coordinate transFormation matrix in the Upper Triangular Form is firstly proposed such that the nonlinear dynamic model can be partially linearized with respect to the unmeasurable states. And, a new type of velocity observers is designed to estimate the unmeasurable velocities for each system. Then, based on the outputs of the velocity observers, we propose distributed control laws that enable the coordinated tracking control system to achieve uniForm global exponential stability (UGES). Both theoretical analysis and numerical simulations are presented to validate the effectiveness of the proposed control scheme. Followed by the original paper, a typo and a mistake is corrected.

  • distributed global output feedback control for a class of euler lagrange systems
    IEEE Transactions on Automatic Control, 2017
    Co-Authors: Qingkai Yang, Hao Fang, Jie Chen, Zhongping Jiang, Ming Cao
    Abstract:

    This paper investigates the distributed tracking control problem for a class of Euler–Lagrange multiagent systems when the agents can only measure the positions. In this case, the lack of the separation principle and the strong nonlinearity in unmeasurable states pose severe technical challenges to global output-feedback control design. To overcome these difficulties, a global nonsingular coordinate transFormation matrix in the Upper Triangular Form is first proposed such that the nonlinear dynamic model can be partially linearized with respect to the unmeasurable states. And, a new type of velocity observers is designed to estimate the unmeasurable velocities for each system. Then, based on the outputs of the velocity observers, we propose distributed control laws that enable the coordinated tracking control system to achieve uniForm global exponential stability. Both theoretical analysis and numerical simulations are presented to validate the effectiveness of the proposed control scheme.

Stanimire Tomov - One of the best experts on this subject based on the ideXlab platform.

  • soft error resilient qr factorization for hybrid system with gpgpu
    Journal of Computational Science, 2013
    Co-Authors: Piotr Luszczek, Jack Dongarra, Stanimire Tomov
    Abstract:

    Abstract The general purpose graphics processing units (GPGPUs) are increasingly deployed for scientific computing due to their perFormance advantages over CPUs. What followed is the fact that fault tolerance has become a more serious concern compared to the period when GPGPUs were used exclusively for graphics applications. Using GPUs and CPUs together in a hybrid computing system increases flexibility and perFormance but also increases the possibility of the computations being affected by soft errors, for example, in the Form of bit flips. In this work, we propose a soft error resilient algorithm for QR factorization on such hybrid systems. Our contributions include: (1) a checkpointing and recovery mechanism for the left-factor Q whose perFormance is scalable on hybrid systems; (2) optimized Givens rotation utilities on GPGPUs to efficiently reduce an Upper Hessenberg matrix to an Upper Triangular Form for the protection of the right factor R ; and (3) a recovery algorithm based on QR update on GPGPUs. Experimental results show that our fault tolerant QR factorization can successfully detect and recover from soft errors in the entire matrix with little overhead on hybrid systems with GPGPUs.

  • soft error resilient qr factorization for hybrid system with gpgpu
    Proceedings of the second workshop on Scalable algorithms for large-scale systems, 2011
    Co-Authors: Piotr Luszczek, Stanimire Tomov, Jack Dongarra
    Abstract:

    The general purpose graphics processing units (GPGPU) are increasingly deployed for scientific computing due to their perFormance advantages over CPUs. As a result, fault tolerance has become a more serious concern compared to the period when GPGPUs were used exclusively for graphics applications. Using GPUs and CPUs together in a hybrid computing system increases flexibility and perFormance but also increases the possibility of the computations being affected by soft errors. In this work, we propose a soft error resilient algorithm for QR factorization on such hybrid systems. Our contributions include (1) a checkpointing and recovery mechanism for the left-factor Q whose perFormance is scalable on hybrid systems; (2) optimized Givens rotation utilities on GPGPUs to efficiently reduce an Upper Hessenberg matrix to an Upper Triangular Form for the protection of the right factor R, and (3) a recovery algorithm based on QR update on GPGPUs. Experimental results show that our fault tolerant QR factorization can success- fully detect and recover from soft errors in the entire matrix with little overhead on hybrid systems with GPGPUs.

  • soft error resilient qr factorization for hybrid system
    University of Tennessee Computer Science Technical Report, 2011
    Co-Authors: Piotr Luszczek, Stanimire Tomov, Jack Dongarra
    Abstract:

    As the general purpose graphics processing units (GPGPU) are increasingly deployed for scientific computing for its raw perFormance advantages compared to CPUs, the fault tolerance issue has started to become more of a concern than before when they were exclusively used for graphics applications. The pairing of GPUs with CPUs to Form a hybrid computing systems for better flexibility and perFormance creates a massive amounts of computations that have a higher possibility to be affected by transient error – a soft error that silently modifies data causing errors to pass unnoticed. This is despite the fact that the newest Fermi generation of GPUs from NVIDIA are equipped with error correcting units to protect their memories. This problem is particularly serious for applications that employ numerical linear algebra since large sections of data are often modified between steps, and therefore even a single error could eventually propagate into a large area of result. In order to give protection to dense linear algebra computations on such hybrid systems, we developed an algorithm that is resilient to soft errors. We chose the right-looking Householder QR factorization as a demonstration of our algorithm for a hybrid system that features both GPUs and CPUs. Algorithm based fault tolerance (ABFT) is used to protect from errors in the trailing matrix and the right factor, while a checkpointing method is used to ensure the left factor is error-free. This work is based on a previous study of fault tolerance in matrix factorizations. Our contribution includes (1) a stable multiple-error checkpointing and recovery mechanism for the left-factor, which is also scalable in perFormance in the hybrid execution environment and does not cause severe perFormance degradation. (2) optimized Givens rotation utilities on the GPU to efficiently reduce an Upper Hessenberg matrix to Upper Triangular Form, and (3) a recovery algorithm based on QR update inside a hybrid system. Experimental results show that, our fault tolerant QR factorization can successfully detect and correct data altered by soft errors in both the left and right factors and we observe a decreasing percentage of overhead as the matrix size grows.