The Experts below are selected from a list of 16617 Experts worldwide ranked by ideXlab platform

George A Constantinides - One of the best experts on this subject based on the ideXlab platform.

  • explicit mpc hard constraint satisfaction under low precision arithmetic
    Control Engineering Practice, 2016
    Co-Authors: Andrea Suardi, Stefano Longo, Eric C Kerrigan, George A Constantinides
    Abstract:

    MPC is becoming increasingly implemented on embedded systems, where low precision computation is preferred either to reduce costs, speedup execution or reduce power consumption. However, in a low precision implementation, constraint satisfaction cannot be guaranteed. To enforce constraint satisfaction under numerical Errors, we adopt tools from Forward Error Analysis to compute an Error bound on the output of the embedded controller. We treat this Error as a state disturbance and use it to inform the design of a constraint-tightening robust controller. The technique is validated via a practical implementation on an FPGA evaluation board.

  • quantization in control systems and Forward Error Analysis of iterative numerical algorithms
    UKACC International Conference on Control, 2010
    Co-Authors: Ammar Hasan, Eric C Kerrigan, George A Constantinides
    Abstract:

    The use of control theory to study iterative algorithms, which can be considered as dynamical systems, opens many opportunities to find new tools for Analysis of algorithms. In this paper we show that results from the study of quantization effects in control systems can be used to find systematic ways for Forward Error Analysis of iterative algorithms. The proposed schemes are applied to the classical iterative methods for solving a system of linear equations. The obtained bounds are compared with bounds given in the numerical Analysis literature.

Eric C Kerrigan - One of the best experts on this subject based on the ideXlab platform.

  • explicit mpc hard constraint satisfaction under low precision arithmetic
    Control Engineering Practice, 2016
    Co-Authors: Andrea Suardi, Stefano Longo, Eric C Kerrigan, George A Constantinides
    Abstract:

    MPC is becoming increasingly implemented on embedded systems, where low precision computation is preferred either to reduce costs, speedup execution or reduce power consumption. However, in a low precision implementation, constraint satisfaction cannot be guaranteed. To enforce constraint satisfaction under numerical Errors, we adopt tools from Forward Error Analysis to compute an Error bound on the output of the embedded controller. We treat this Error as a state disturbance and use it to inform the design of a constraint-tightening robust controller. The technique is validated via a practical implementation on an FPGA evaluation board.

  • quantization in control systems and Forward Error Analysis of iterative numerical algorithms
    UKACC International Conference on Control, 2010
    Co-Authors: Ammar Hasan, Eric C Kerrigan, George A Constantinides
    Abstract:

    The use of control theory to study iterative algorithms, which can be considered as dynamical systems, opens many opportunities to find new tools for Analysis of algorithms. In this paper we show that results from the study of quantization effects in control systems can be used to find systematic ways for Forward Error Analysis of iterative algorithms. The proposed schemes are applied to the classical iterative methods for solving a system of linear equations. The obtained bounds are compared with bounds given in the numerical Analysis literature.

Robert Kleinberg - One of the best experts on this subject based on the ideXlab platform.

  • fast matrix multiplication is stable
    Numerische Mathematik, 2007
    Co-Authors: James Demmel, Olga Holtz, Ioana Dumitriu, Robert Kleinberg
    Abstract:

    We perform Forward Error Analysis for a large class of recursive matrix multiplication algorithms in the spirit of Bini and Lotti [Numer. Math. 36:63–72, 1980]. As a consequence of our Analysis, we show that the exponent of matrix multiplication (the optimal running time) can be achieved by numerically stable algorithms. We also show that new group-theoretic algorithms proposed in Cohn and Umans [Foundations of Computer Science, 44th Annual IEEE Symposium, pp. 438–449, 2003] and Cohn et al. [Foundations of Computer Science, 46th Annual IEEE Symposium, pp. 379–388, 2005] are all included in the class of algorithms to which our Analysis applies, and are therefore numerically stable. We perform detailed Error Analysis for three specific fast group-theoretic algorithms.

  • fast matrix multiplication is stable
    arXiv: Numerical Analysis, 2006
    Co-Authors: James Demmel, Olga Holtz, Ioana Dumitriu, Robert Kleinberg
    Abstract:

    We perform Forward Error Analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a consequence of our Analysis, we show that the exponent of matrix multiplication (the optimal running time) can be achieved by numerically stable algorithms. We also show that new group-theoretic algorithms proposed in [H. Cohn, and C. Umans, A group-theoretic approach to fast matrix multiplication, FOCS 2003, 438--449] and [H. Cohn, R. Kleinberg, B. Szegedy and C. Umans, Group-theoretic algorithms for matrix multiplication, FOCS 2005, 379--388] are all included in the class of algorithms to which our Analysis applies, and are therefore numerically stable. We perform detailed Error Analysis for three specific fast group-theoretic algorithms.

James Demmel - One of the best experts on this subject based on the ideXlab platform.

  • fast matrix multiplication is stable
    Numerische Mathematik, 2007
    Co-Authors: James Demmel, Olga Holtz, Ioana Dumitriu, Robert Kleinberg
    Abstract:

    We perform Forward Error Analysis for a large class of recursive matrix multiplication algorithms in the spirit of Bini and Lotti [Numer. Math. 36:63–72, 1980]. As a consequence of our Analysis, we show that the exponent of matrix multiplication (the optimal running time) can be achieved by numerically stable algorithms. We also show that new group-theoretic algorithms proposed in Cohn and Umans [Foundations of Computer Science, 44th Annual IEEE Symposium, pp. 438–449, 2003] and Cohn et al. [Foundations of Computer Science, 46th Annual IEEE Symposium, pp. 379–388, 2005] are all included in the class of algorithms to which our Analysis applies, and are therefore numerically stable. We perform detailed Error Analysis for three specific fast group-theoretic algorithms.

  • fast matrix multiplication is stable
    arXiv: Numerical Analysis, 2006
    Co-Authors: James Demmel, Olga Holtz, Ioana Dumitriu, Robert Kleinberg
    Abstract:

    We perform Forward Error Analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a consequence of our Analysis, we show that the exponent of matrix multiplication (the optimal running time) can be achieved by numerically stable algorithms. We also show that new group-theoretic algorithms proposed in [H. Cohn, and C. Umans, A group-theoretic approach to fast matrix multiplication, FOCS 2003, 438--449] and [H. Cohn, R. Kleinberg, B. Szegedy and C. Umans, Group-theoretic algorithms for matrix multiplication, FOCS 2005, 379--388] are all included in the class of algorithms to which our Analysis applies, and are therefore numerically stable. We perform detailed Error Analysis for three specific fast group-theoretic algorithms.

Zhendong Su - One of the best experts on this subject based on the ideXlab platform.

  • automated backward Error Analysis for numerical code
    Conference on Object-Oriented Programming Systems Languages and Applications, 2015
    Co-Authors: Zhoulai Fu, Zhendong Su
    Abstract:

    Numerical code uses floating-point arithmetic and necessarily suffers from roundoff and truncation Errors. Error Analysis is the process to quantify such uncertainty in the solution to a problem. Forward Error Analysis and backward Error Analysis are two popular paradigms of Error Analysis. Forward Error Analysis is more intuitive and has been explored and automated by the programming languages (PL) community. In contrast, although backward Error Analysis is more preferred by numerical analysts and the foundation for numerical stability, it is less known and unexplored by the PL community. To fill the gap, this paper presents an automated backward Error Analysis for numerical code to empower both numerical analysts and application developers. In addition, we use the computed backward Error results to also compute the condition number, an important quantity recognized by numerical analysts for measuring how sensitive a function is to changes or Errors in the input. Experimental results on Intel X87 FPU functions and widely-used GNU C Library functions demonstrate that our Analysis is effective at analyzing the accuracy of floating-point programs.