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14
Spectral residual method without gradient information for solving largescale nonlinear systems: Theory and experiments
, 2004
"... Abstract. A fully derivativefree spectral residual method for solving largescale nonlinear systems of equations is presented. It uses in a systematic way the residual vector as a search direction, a spectral steplength that produces a nonmonotone process and a globalization strategy that allows for ..."
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Cited by 23 (5 self)
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Abstract. A fully derivativefree spectral residual method for solving largescale nonlinear systems of equations is presented. It uses in a systematic way the residual vector as a search direction, a spectral steplength that produces a nonmonotone process and a globalization strategy that allows for this nonmonotone behavior. The global convergence analysis of the combined scheme is presented. An extensive set of numerical experiments that indicate that the new combination is competitive and frequently better than wellknown NewtonKrylov methods for largescale problems is also presented. 1.
Two Classes of Multisecant Methods for Nonlinear Acceleration ∗
, 2007
"... Many applications in science and engineering lead to models which require solving largescale fixed point problems, or equivalently, systems of nonlinear equations. Several successful techniques for handling such problems are based on quasiNewton methods that implicitly update the approximate Jacob ..."
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Cited by 21 (0 self)
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Many applications in science and engineering lead to models which require solving largescale fixed point problems, or equivalently, systems of nonlinear equations. Several successful techniques for handling such problems are based on quasiNewton methods that implicitly update the approximate Jacobian or inverse Jacobian to satisfy a certain secant condition. We present two classes of multisecant methods which allows to take into account a variable number of secant equations at each iteration. The first is the Broydenlike class, of which Broyden’s family is a subclass, and Anderson mixing is a particular member. The second class is that of the nonlinear EirolaNevanlinnatype methods. This work was motivated by a problem in electronic structure calculations, whereby a fixed point iteration, known as the selfconsistent field (SCF) iteration, is accelerated by various strategies termed ‘mixing’. 1
An efficient and effective nonlinear solver in a parallel software for large scale petroleum reservoir simulation
 Int. J. Numer. Anal. Model
, 2005
"... Abstract. We study a parallel NewtonKrylovSchwarz (NKS) based algorithm for solving large sparse systems resulting from a fully implicit discretization of partial differential equations arising from petroleum reservoir simulations. Our NKS algorithm is designed by combining an inexact Newton metho ..."
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Cited by 2 (0 self)
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Abstract. We study a parallel NewtonKrylovSchwarz (NKS) based algorithm for solving large sparse systems resulting from a fully implicit discretization of partial differential equations arising from petroleum reservoir simulations. Our NKS algorithm is designed by combining an inexact Newton method with a rank2 updated quasiNewton method. In order to improve the computational efficiency, both DDM and SPMD parallelism strategies are adopted. The effectiveness of the overall algorithm depends heavily on the performance of the linear preconditioner, which is made of a combination of several preconditioning components including AMG, relaxed ILU, up scaling, additive Schwarz, CRPlike(constraint residual preconditioning), Watts correction, Shur complement,
Dynamic response simulation for a nonlinear system
 Journal of Sound and Vibration
"... Laboratory simulation testing has for many years contributed significantly to the durability and quality of motor vehicles. Most sophisticated test rigs use an iterative algorithm that generates the input drive files that reproduce service environments under laboratory conditions. Essentially the al ..."
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Laboratory simulation testing has for many years contributed significantly to the durability and quality of motor vehicles. Most sophisticated test rigs use an iterative algorithm that generates the input drive files that reproduce service environments under laboratory conditions. Essentially the algorithm solves a nonlinear, multiple channel dynamic system. In this paper, the nonlinear problem is recast as a system of algebraic equations. This mathematical framework allows the application of alternative but well understood solution techniques. Using mathematical simulations, conclusions are drawn concerning the choice of iteration gain in the current algorithm and the better performance of alternative numerical solution procedures.
GSM METHOD
"... A generalization of secant methods for solving nonlinear systems of equations ..."
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A generalization of secant methods for solving nonlinear systems of equations
Dynamic Response Simulation Through System Identification
"... Nonlinear dynamic systems, such as those associated with structural testing of vehicles, are considered. The vehicle, or a substructure, is mounted in a test rig that is normally driven by servohydraulic actuators. The specimen and test rig form a nonlinear dynamic system. These test systems assu ..."
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Nonlinear dynamic systems, such as those associated with structural testing of vehicles, are considered. The vehicle, or a substructure, is mounted in a test rig that is normally driven by servohydraulic actuators. The specimen and test rig form a nonlinear dynamic system. These test systems assure the durability of vehicles by reproducing a structural response time history that has been measured in a road test of a vehicle. For this, a force or displacement input to the actuators ’ control system must be determined as a function of time. Current practice employs an iterative algorithm, using a frequency response function to represent the system. The conventional iteration is a particular version of well established numerical techniques for solving nonlinear systems. However, the success of the iteration is dependent on the degree of nonlinearity and on the level of noise in the signals coming from the system. This paper advocates identifying the system to improve its representation in the iterative algorithm. The theory underpinning the alternative algorithm is presented and a comparison is made between the performances of the two algorithms, using computer simulations based on Duffing’s equation. These simulations show that, even for this simple model, the alternative algorithm is faster, more reliable and more tolerant of response noise. Key words: Laboratory simulation testing, dynamic system, spectral analysis, random signal, Duffing’s equation, nonlinear algebraic equations, numerical