Topic
Linear approximation
About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.
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TL;DR: In this article, the authors present an intuitive on-line tuning strategy for linear MPC algorithms based on the linear approximation between the closed-loop predicted output and the MPC tuning parameters.
108 citations
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TL;DR: An adaptive linear approximation algorithm for copositive programs is derived that can be guided adaptively through the objective function, yielding a good approximation in those parts of the cone that are relevant for the optimization and only a coarse approximation inThose parts that are not.
Abstract: We study linear optimization problems over the cone of copositive matrices. These problems appear in nonconvex quadratic and binary optimization; for instance, the maximum clique problem and other combinatorial problems can be reformulated as such problems. We present new polyhedral inner and outer approximations of the copositive cone which we show to be exact in the limit. In contrast to previous approximation schemes, our approximation is not necessarily uniform for the whole cone but can be guided adaptively through the objective function, yielding a good approximation in those parts of the cone that are relevant for the optimization and only a coarse approximation in those parts that are not. Using these approximations, we derive an adaptive linear approximation algorithm for copositive programs. Numerical experiments show that our algorithm gives very good results for certain nonconvex quadratic problems.
108 citations
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TL;DR: In this article, the nonlinear response of an atom to a near-resonant light pulse is studied using a novel approximation scheme, which reduces to the well-known rate equations.
Abstract: The nonlinear response of an atom to a near-resonant light pulse is studied using a novel approximation scheme. In first order, the approximate solution reduces to the well-known rate equations. The second-order approximation contains Grischkowsky's adiabatic-following approximation. In each order, the approximate solution of the Bloch equations is presented with a closed-form expression for the error that can be used to investigate its range of validity.
108 citations
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TL;DR: In this article, an improved Fast Implicit Finite Difference (FIFD) algorithm was proposed to solve second-order equations in a (quasi-) exact way for the square scheme.
108 citations
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TL;DR: The preconditionded conjugate gradient method for solving a linear algebraic system of equations is recast to a form that permits sequential element-by-element calculations suitable for computations with finite element methods.
Abstract: The preconditionded conjugate gradient method for solving a linear algebraic system of equations is recast to a form that permits sequential element-by-element calculations suitable for computations with finite element methods. This strategy has been implemented for solving the linear systems arising in a finite element approximation for the standard test example of Laplace's equation. The element-by-element strategy has also been applied to the sequence of linear systems obtained using a successive approximation scheme for a representative class of nonlinear problems. Little storage is needed for these schemes, and test computations have been made on microprocessor, minicomputer, main-frame computers and special processors. The approach also appears appealing for calculations on parallel processors since individual element computations can be done in parallel.
107 citations