The Experts below are selected from a list of 7797 Experts worldwide ranked by ideXlab platform
Moritz Diehl - One of the best experts on this subject based on the ideXlab platform.
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a real time algorithm for nonlinear receding horizon control using multiple shooting and continuation Krylov Method
International Journal of Robust and Nonlinear Control, 2009Co-Authors: Y Shimizu, Toshiyuki Ohtsuka, Moritz DiehlAbstract:In this paper, we propose a real-time algorithm for nonlinear receding horizon control using multiple shooting and the continuation/GMRES Method. Multiple shooting is expected to improve numerical accuracy in calculations for solving boundary value problems. The continuation Method is combined with a Krylov Subspace Method, GMRES, to update unknown quantities by solving a linear equation. At the same time, we apply condensing, which reduces the size of the linear equation, to speed up numerical calculations. A numerical example shows that both numerical accuracy and computational speed improve using the proposed algorithm by combining multiple shooting with condensing. Copyright © 2008 John Wiley & Sons, Ltd.
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nonlinear receding horizon control of an underactuated hovercraft with a multiple shooting based algorithm
International Conference on Control Applications, 2006Co-Authors: Y Shimizu, Toshiyuki Ohtsuka, Moritz DiehlAbstract:In this paper, we propose a real-time algorithm for nonlinear receding horizon control using multiple shooting and the continuation/GMRES Method. The multiple shooting is expected to improve numerical accuracy and stability in calculations for solving a boundary value problem. The continuation Method is combined with a Krylov-Subspace Method, GMRES, to update unknown quantities by solving a linear equation. At the same time, we apply condensing, which reduces the size of the linear equation, to speed up numerical calculations. The proposed algorithm is applied to an underactuated hovercraft. Computational results show that the proposed algorithm is superior to a conventional one in the numerical accuracy and stability.
K Jbilou - One of the best experts on this subject based on the ideXlab platform.
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a generalized matrix Krylov Subspace Method for tv regularization
Journal of Computational and Applied Mathematics, 2020Co-Authors: Abdeslem Hafid Bentbib, El M Guide, K JbilouAbstract:Abstract This paper presents efficient algorithms to solve both TV/L1 and TV/L2 models of images contaminated by blur and noise. The unconstrained structure of the problems suggests that one can solve a constrained optimization problem by transforming the original unconstrained minimization problem to an equivalent constrained minimization one. An augmented Lagrangian Method is developed to handle the constraints when the model is given with matrix variables, and an alternating direction Method (ADM) is used to iteratively find solutions of the subproblems. The solutions of some subproblems are belonging to Subspaces generated by application of successive orthogonal projections onto a class of generalized matrix Krylov Subspaces of increasing dimension. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed algorithms.
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a generalized matrix Krylov Subspace Method for tv regularization
arXiv: Numerical Analysis, 2018Co-Authors: Abdeslem Hafid Bentbib, El M Guide, K JbilouAbstract:This paper presents an efficient algorithm to solve total variation (TV) regularizations of images contaminated by a both blur and noise. The unconstrained structure of the problem suggests that one can solve a constrained optimization problem by transforming the original unconstrained minimization problem to an equivalent constrained minimization one. An augmented Lagrangian Method is developed to handle the constraints when the model is given with matrix variables, and an alternating direction Method (ADM) is used to iteratively find solutions. The solutions of some sub-problems are belonging to Subspaces generated by application of successive orthogonal projections onto a class of generalized matrix Krylov Subspaces of increasing dimension.
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a note on the numerical approximate solutions for generalized sylvester matrix equations with applications
Applied Mathematics and Computation, 2008Co-Authors: A Bouhamidi, K JbilouAbstract:Abstract In the present paper, we propose a Krylov Subspace Method for solving large and sparse generalized Sylvester matrix equations. The proposed Method is an iterative projection Method onto matrix Krylov Subspaces. As a particular case, we show how to adapt the ILU and the SSOR preconditioners for solving large Sylvester matrix equations. Numerical examples and applications to some PDE’s will be given.
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low rank approximate solutions to large sylvester matrix equations
Applied Mathematics and Computation, 2006Co-Authors: K JbilouAbstract:In the present paper, we propose an Arnoldi-based Method for solving large and sparse Sylvester matrix equations with low rank right hand sides. We will show how to extract low-rank approximations via a matrix Krylov Subspace Method. We give some theoretical results such an expression of the exact solution and upper bounds for the norm of the error and for the residual. Numerical experiments will also be given to show the effectiveness of the proposed Method.
Sheldon X D Tan - One of the best experts on this subject based on the ideXlab platform.
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fast em stress evolution analysis using Krylov Subspace Method
2019Co-Authors: Sheldon X D Tan, Mehdi B Tahoori, Taeyoung Kim, Shengcheng Wang, Zeyu Sun, Saman KiamehrAbstract:As mentioned in Chap. 2, the stress in the interconnect tree is not independent for multi-segment interconnect trees. More accurate EM modeling and analysis techniques are needed. Recently more accurate physics-based EM models and assessment techniques have been proposed. In Huang et al. (Proceedings of the Design Automation Conference (DAC), June 2014; IEEE Trans Comput Aided Des Integr Circuits Syst 35(11):1848–1861, 2016), a compact time to failure model based on the Korhonen’s equation, mentioned in Chap. 2 was proposed. Initially, this EM model worked for only a single wire segment but has been extended to deal with multi-segment interconnect trees based on the projected steady-state stress.
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fast electromigration stress evolution analysis for interconnect trees using Krylov Subspace Method
IEEE Transactions on Very Large Scale Integration Systems, 2018Co-Authors: Chase Cook, Zeyu Sun, Ertugrul Demircan, Mehul D Shroff, Sheldon X D TanAbstract:Electromigration effects are a key failure mechanism for copper-based dual damascene interconnects wires in semiconductor technologies. However, accurately predicting the time-to-failure for a complicated interconnect tree in a VLSI interconnect layout requires detailed knowledge of the stress evolutions over time, and is subject to time-varying currents and temperature. This is a challenging problem as one needs to solve the stress-based partial differential equations (PDEs) in the time domain for confined copper damascene interconnect trees for both void nucleation and void growth phases. To mitigate this problem, we propose a novel Krylov Subspace-based Method for fast numerical solutions to the stress PDEs. The new approach, which we call FastEM , is based on the finite-difference Method which is used to first discretize the PDEs into linear time-invariant ordinary differential equations (ODEs). After discretization, a modified Krylov Subspace-based reduction technique is applied in the frequency domain to reduce the size of the original system matrices so that they can be efficiently simulated in the time domain. The FastEM can perform the simulation process for both void nucleation and void growth phases under piecewise constant linear current density inputs and time-varying stressing temperatures. Furthermore, we show that the steady-state response of stress diffusion equations can be obtained from the resulting ODE system in the frequency domain, which agrees with the recently proposed voltage-based EM analysis Method for EM immortality checks. Numerical results show that the proposed Method can lead to about 1–2 orders of magnitude speed-up over existing finite-difference time-domain-based Methods on large interconnect trees for both void nucleation and growth phases with negligible errors. We further show that for most of the interconnect trees tested; we only need a small number of dominant poles for sufficient accuracy.
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statistical power grid analysis by stochastic extended Krylov Subspace Method
2012Co-Authors: Ruijing Shen, Sheldon X D TanAbstract:In this chapter, we present a stochastic Method for analyzing the voltage drop variations of on-chip power grid networks with log-normal leakage current variations, which is called StoEKS and which still applies the spectral-stochastic-Method to solve for the variational responses. But different from the existing spectral-stochastic-based simulation Method, the EKS Method [191, 177] is employed to compute variational responses using the augmented matrices consisting of the coefficients of Hermite polynomials. Our work is inspired by recent spectral-stochastic-based model order reduction Method 2[214]. We apply this work to the variational analysis of on-chip power grid networks considering the variational leakage currents with the log-normal distribution.
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fast variational analysis of on chip power grids by stochastic extended Krylov Subspace Method
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2008Co-Authors: Sheldon X D Tan, Yici Cai, Xianlong HongAbstract:This paper proposes a novel stochastic Method for analyzing the voltage drop variations of on-chip power grid networks, considering lognormal leakage current variations. The new Method, called StoEKS, applies Hermite polynomial chaos to represent the random variables in both power grid networks and input leakage currents. However, different from the existing orthogonal polynomial-based stochastic simulation Method, extended Krylov Subspace (EKS) Method is employed to compute variational responses from the augmented matrices consisting of the coefficients of Hermite polynomials. Our contribution lies in the acceleration of the spectral stochastic Method using the EKS Method to fast solve the variational circuit equations for the first time. By using the reduction technique, the new Method partially mitigates increased circuit-size problem associated with the augmented matrices from the Galerkin-based spectral stochastic Method. Experimental results show that the proposed Method is about two-order magnitude faster than the existing Hermite PC-based simulation Method and many order of magnitudes faster than Monte Carlo Methods with marginal errors. StoEKS is scalable for analyzing much larger circuits than the existing Hermit PC-based Methods.
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stochastic extended Krylov Subspace Method for variational analysis of on chip power grid networks
International Conference on Computer Aided Design, 2007Co-Authors: Sheldon X D Tan, Pu Liu, Jian Cui, Yici Cai, Xianlong HongAbstract:In this paper, we propose a novel stochastic Method for analyzing the voltage drop variations of on-chip power grid networks with log-normal leakage current variations. The new Method, called StoEKS, applies Hermite polynomial chaos (PC) to represent the random variables in both power grid networks and input leakage currents. But different from the existing Hermit PC based stochastic simulation Method, extended Krylov Subspace Method (EKS) is employed to compute variational responses using the augmented matrices consisting of the coefficients of Hermite polynomials. Our contribution lies in the combination of the statistical spectrum Method with the extended Krylov Subspace Method to fast solve the variational circuit equations for the first time. Experimental results show that the proposed Method is about two-order magnitude faster than the existing Her-mite PC based simulation Method and more order of magnitudes faster than Monte Carlo Methods with marginal errors. StoEKS also can analyze much larger circuits than the exiting Hermit PC based Methods.
Stefan Guttel - One of the best experts on this subject based on the ideXlab platform.
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rational Krylov approximation of matrix functions numerical Methods and optimal pole selection
Gamm-mitteilungen, 2013Co-Authors: Stefan GuttelAbstract:Matrix functions are a central topic of linear algebra, and problems of their numerical approximation appear increasingly often in scientific computing. We review various rational Krylov Methods for the computation of large-scale matrix functions. Emphasis is put on the rational Arnoldi Method and variants thereof, namely, the extended Krylov Subspace Method and the shift-and-invert Arnoldi Method, but we also discuss the nonorthogonal generalized Leja point (or PAIN) Method. The issue of optimal pole selection for rational Krylov Methods applied for approximating the resolvent and exponential function, and functions of Markov type, is treated in some detail. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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implementation of a restarted Krylov Subspace Method for the evaluation of matrix functions
Linear Algebra and its Applications, 2008Co-Authors: M Afanasjew, Michael Eiermann, Oliver G Ernst, Stefan GuttelAbstract:A new implementation of restarted Krylov Subspace Methods for evaluating f (A)b for a function f ,a matrix A and a vector b is proposed. In contrast to an implementation proposed previously, it requires constant work and constant storage space per restart cycle. The convergence behavior of this scheme is discussed and a new stopping criterion based on an error indicator is given. The performance of the implementation is illustrated for three parabolic initial value problems, requiring the evaluation of exp(A)b.
Thomas Zemen - One of the best experts on this subject based on the ideXlab platform.
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Krylov Subspace Method based low complexity mimo multi user receiver for time variant channels
Personal Indoor and Mobile Radio Communications, 2006Co-Authors: Charlotte Dumard, Thomas ZemenAbstract:We consider the uplink of a time-variant multiple-input-multiple-output (MIMO) multi-user (MU) multi-carrier (MC) code division multiple access (CDMA) system. The linear minimum mean square error (LMMSE) filters for channel estimation and multi-user detection at the receiver side require too high complexity to be implementable in a system operating in time-variant channels. We develop a low-complexity implementation of an LMMSE filter based on the Krylov Subspace Method. We are able to reduce the computational complexity by one order of magnitude. Furthermore, in a system with K users having N T transmit antennas, parallelization of the computations of the multi-user detector into KNT branches is achieved as well as considerable storage reduction. We discuss more specifically a fully loaded system (the number of subcarriers N is equal to the number of users K) with NT = 2 transmit antennas per user, NR = 4 receive antennas and K = N = 64
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integration of the Krylov Subspace Method in an iterative multi user detector for time variant channels
International Conference on Acoustics Speech and Signal Processing, 2006Co-Authors: Charlotte Dumard, Thomas ZemenAbstract:Iterative multi-user detection and time-variant channel estimation in a multi-carrier (MC) code division multiple access (CDMA) uplink requires high computational complexity. This is mainly due to the linear minimum mean square error (LMMSE) filters that are used for multi-user detection and time-variant channel estimation. Krylov Subspace Methods allow for an efficient implementation of the LMMSE filter. We show that a suitable chosen starting value, exploiting the iterative receiver structure, allows for a further speedup of the Krylov Method. We achieve a complexity reduction by more than one order of magnitude. The Krylov Subspace Method allows a parallelization of the computations of the multi-user detector, while keeping the receiver performance constant. Numerical simulation results for a fully loaded system with K = 64 users are presented.
