The Experts below are selected from a list of 7518 Experts worldwide ranked by ideXlab platform

Marc Lambert - One of the best experts on this subject based on the ideXlab platform.

  • Stochastic Matrices and Lp Norms : New Algorithms for Solving Ill-conditioned Linear Systems of Equations
    ESAIM: Proceedings, 2007
    Co-Authors: Riadh Zorgati, Wim Stefanus Van Ackooij, Marc Lambert
    Abstract:

    We propose new iterative algorithms for solving a system of linear equations, possibly singular and inconsistent, presenting outstanding performances regarding ill-conditioning and error propagation. The basis of our approach is constructing with the l 1 norm, a Preconditioning Matrix C (an approximation of a generalized inverse of the Matrix) such that the preconditioned Matrix CA is stochastic. This property allows us to retrieve, in an original way, the Schultz-Hotelling-Bodewig's algorithm of iterative refinement of the approximate inverse of a Matrix. The approach, valid for non-negative matrices, is then generalized to any complex, rectangular Matrix. We are then able to compute a generalized inverse of any Matrix and this inverse is fit for use in classical solving schemes such as : Richardson-Tanabe, Schultz-Hotelling-Bodewig, preconditioned conjugate gradients and also in the Kaczmarz scheme (that we have generalized using l p norms). Regarding the obtained results on pathological well-known test-cases such as Hilbert and Nakasaka matrices, some of the proposed algorithms are empirically shown to be more efficient than the known classical techniques.

  • Stochastic matrices and $L_{p}$ norms: new algorithms for solving ill-conditioned linear systems of equations
    2007
    Co-Authors: Riadh Zorgati, Wim Stefanus Van Ackooij, Marc Lambert
    Abstract:

    We propose new iterative algorithms for solving a system of linear equations, possibly singular and inconsistent, presenting outstanding performances regarding ill-conditioning and error propagation. The basis of our approach is constructing with the l1 norm, a Preconditioning Matrix C (an approximation of a generalized inverse of the Matrix) such that the preconditioned Matrix CA is stochastic. This property allows us to retrieve, in an original way, the Schultz-Hotelling-Bodewig's algorithm of iterative refinement of the approximate inverse of a Matrix. The approach, valid for non-negative matrices, is then generalized to any complex, rectangular Matrix. We are then able to compute a generalized inverse of any Matrix and this inverse is fit for use in classical solving schemes such as : Richardson-Tanabe, Schultz-Hotelling-Bodewig, preconditioned conjugate gradients and also in the Kaczmarz scheme (that we have generalized using lp norms). Regarding the obtained results on pathological well-known test-cases such as Hilbert and Nakasaka matrices, some of the proposed algorithms are empirically shown to be more efficient than the known classical techniques.

Eli Turkel - One of the best experts on this subject based on the ideXlab platform.

  • Preconditioning techniques in computational fluid dynamics
    Annual Review of Fluid Mechanics, 1999
    Co-Authors: Eli Turkel
    Abstract:

    ▪ Abstract An overview of Preconditioning for the steady-state compressible inviscid fluid dynamic equations is presented. Extensions to the Navier-Stokes equations are also considered. These preconditioners are necessary for many algorithms in order to have the correct behavior at low speeds and to converge to the solution of the incompressible equations as the Mach number goes to zero. In addition, the Preconditioning accelerates the convergence to a steady state for problems in which a significant portion of the flow is low speed. This low speed preconditioner can be combined with Jacobi and line preconditioners to damp high frequencies at all speeds. This is necessary for use with multigrid methods. Such combined methods are also better at accelerating problems with high aspect ratios. Details of the implementation are presented including several different variants for the Preconditioning Matrix.

  • Preconditioning techniques in computational fluid dynamics
    Annual Review of Fluid Mechanics, 1999
    Co-Authors: Eli Turkel
    Abstract:

    ▪ Abstract An overview of Preconditioning for the steady-state compressible inviscid fluid dynamic equations is presented. Extensions to the Navier-Stokes equations are also considered. These preconditioners are necessary for many algorithms in order to have the correct behavior at low speeds and to converge to the solution of the incompressible equations as the Mach number goes to zero. In addition, the Preconditioning accelerates the convergence to a steady state for problems in which a significant portion of the flow is low speed. This low speed preconditioner can be combined with Jacobi and line preconditioners to damp high frequencies at all speeds. This is necessary for use with multigrid methods. Such combined methods are also better at accelerating problems with high aspect ratios. Details of the implementation are presented including several different variants for the Preconditioning Matrix.

Sergio Grammatico - One of the best experts on this subject based on the ideXlab platform.

  • ECC - A damped forward–backward algorithm for stochastic generalized Nash equilibrium seeking
    2020 European Control Conference (ECC), 2020
    Co-Authors: Barbara Franci, Sergio Grammatico
    Abstract:

    We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected–value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward– backward operator splitting and a suitable Preconditioning Matrix. Specifically, we apply this method to the stochastic GNEP, where, at each iteration, the expected value of the pseudo–gradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of our proposed algorithm if the sample size grows large enough.

  • A damped forward-backward algorithm for stochastic generalized Nash equilibrium seeking.
    arXiv: Optimization and Control, 2019
    Co-Authors: Barbara Franci, Sergio Grammatico
    Abstract:

    We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward-backward operator splitting and a suitable Preconditioning Matrix. Specifically, we apply this method to the stochastic GNEP, where, at each iteration, the expected value of the pseudo-gradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of our proposed algorithm if the sample size grows large enough.

R. S. Chen - One of the best experts on this subject based on the ideXlab platform.

  • Preconditioning Matrix Interpolation Technique for Fast Analysis of Scattering Over Broad Frequency Band
    IEEE Transactions on Antennas and Propagation, 2010
    Co-Authors: D. Z. Ding, R. S. Chen
    Abstract:

    A hybrid interpolation method is proposed for the fast analysis of the radar cross-section (RCS) over a broad frequency band by use of the Matrix interpolation method. In order to efficiently compute electromagnetic scattering, the general minimal residual (GMRES) iterative solver is applied to compute the coefficients of Rao-Wilton-Glisson (RWG) basis functions and the sparse approximate inversion (SAI) Preconditioning technique is used to accelerate the iterative solver. Moreover, both the near field impedance and SAI Preconditioning matrices are interpolated at intermediate frequencies over a relatively large frequency band with rational function interpolation technique. Therefore, a lot of time can be saved for the calculation of both the near field impedance and Preconditioning matrices. Numerical results demonstrate that this hybrid method is efficient for wideband RCS calculation with high accuracy.

Riadh Zorgati - One of the best experts on this subject based on the ideXlab platform.

  • Stochastic Matrices and Lp Norms : New Algorithms for Solving Ill-conditioned Linear Systems of Equations
    ESAIM: Proceedings, 2007
    Co-Authors: Riadh Zorgati, Wim Stefanus Van Ackooij, Marc Lambert
    Abstract:

    We propose new iterative algorithms for solving a system of linear equations, possibly singular and inconsistent, presenting outstanding performances regarding ill-conditioning and error propagation. The basis of our approach is constructing with the l 1 norm, a Preconditioning Matrix C (an approximation of a generalized inverse of the Matrix) such that the preconditioned Matrix CA is stochastic. This property allows us to retrieve, in an original way, the Schultz-Hotelling-Bodewig's algorithm of iterative refinement of the approximate inverse of a Matrix. The approach, valid for non-negative matrices, is then generalized to any complex, rectangular Matrix. We are then able to compute a generalized inverse of any Matrix and this inverse is fit for use in classical solving schemes such as : Richardson-Tanabe, Schultz-Hotelling-Bodewig, preconditioned conjugate gradients and also in the Kaczmarz scheme (that we have generalized using l p norms). Regarding the obtained results on pathological well-known test-cases such as Hilbert and Nakasaka matrices, some of the proposed algorithms are empirically shown to be more efficient than the known classical techniques.

  • Stochastic matrices and $L_{p}$ norms: new algorithms for solving ill-conditioned linear systems of equations
    2007
    Co-Authors: Riadh Zorgati, Wim Stefanus Van Ackooij, Marc Lambert
    Abstract:

    We propose new iterative algorithms for solving a system of linear equations, possibly singular and inconsistent, presenting outstanding performances regarding ill-conditioning and error propagation. The basis of our approach is constructing with the l1 norm, a Preconditioning Matrix C (an approximation of a generalized inverse of the Matrix) such that the preconditioned Matrix CA is stochastic. This property allows us to retrieve, in an original way, the Schultz-Hotelling-Bodewig's algorithm of iterative refinement of the approximate inverse of a Matrix. The approach, valid for non-negative matrices, is then generalized to any complex, rectangular Matrix. We are then able to compute a generalized inverse of any Matrix and this inverse is fit for use in classical solving schemes such as : Richardson-Tanabe, Schultz-Hotelling-Bodewig, preconditioned conjugate gradients and also in the Kaczmarz scheme (that we have generalized using lp norms). Regarding the obtained results on pathological well-known test-cases such as Hilbert and Nakasaka matrices, some of the proposed algorithms are empirically shown to be more efficient than the known classical techniques.