Showing papers on "Linear approximation published in 2004"
TL;DR: An algorithm for the construction of an explicit piecewise linear state feedback approximation to nonlinear constrained receding horizon control that allows such controllers to be implemented via an efficient binary tree search, avoiding real-time optimization.
252 citations
15 Aug 2004
TL;DR: In this paper, the authors developed a formal statistical framework for block cipher attacks based on this technique and derived explicit and compact gain formulas for generalized versions of Matsui's Algorithm 1 and Algorithm 2.
Abstract: In this paper we study the long standing problem of information extraction from multiple linear approximations. We develop a formal statistical framework for block cipher attacks based on this technique and derive explicit and compact gain formulas for generalized versions of Matsui’s Algorithm 1 and Algorithm 2. The theoretical framework allows both approaches to be treated in a unified way, and predicts significantly improved attack complexities compared to current linear attacks using a single approximation. In order to substantiate the theoretical claims, we benchmarked the attacks against reduced-round versions of DES and observed a clear reduction of the data and time complexities, in almost perfect correspondence with the predictions. The complexities are reduced by several orders of magnitude for Algorithm 1, and the significant improvement in the case of Algorithm 2 suggests that this approach may outperform the currently best attacks on the full DES algorithm.
127 citations
TL;DR: The equilibrated residual method for a posteriori error estimation is extended to nonconforming finite element schemes for the approximation of linear second order elliptic equations where the permeability coefficient is allowed to undergo large jumps in value across interfaces between differing media.
Abstract: The equilibrated residual method for a posteriori error estimation is extended to nonconforming finite element schemes for the approximation of linear second order elliptic equations where the permeability coefficient is allowed to undergo large jumps in value across interfaces between differing media. The estimator is shown to provide a computable upper bound on the error and, up to a constant depending only on the geometry, provides two-sided bounds on the error. The robustness of the estimator is also studied and the dependence of the constant on the jumps in permeability is given explicitly.
121 citations
Book•
17 Sep 2004
TL;DR: The best ebooks about Approximation Theory Using Positive Linear Operators that you can get for free here by download this approximation theory using positive linear operators and save to your desktop.
Abstract: The best ebooks about Approximation Theory Using Positive Linear Operators that you can get for free here by download this Approximation Theory Using Positive Linear Operators and save to your desktop. This ebooks is under topic such as approximation theory using positive linear operators statistical fuzzy approximation theory by fuzzy positive approximation theory using positive linear operators a-summation process and korovkin-type approximation approximation theory using positive linear operators uniform weighted approximation by positive linear operators approximation theory using positive linear operators approximation by certain positive linear operators utcluj statistical approximation by positive linear operators on the a-statistical approximation by sequences of k uniform approximation in weighted spaces using some approximation of analytical functions by sequences of k statistical approximation properties of a generalization 1 maximum likelihood estimation of functionals of discrete approximation of functions of two variables by some linear approximation of functions of two variables by some linear weighted approximation by positive linear operators contributions to the approximation of functions evaluation of the approximation order by positive linear statistical convergence applied to korovkin-type higher order generalization of positive linear operators on linear and positive operators wseas statistical approximation for new positive linear i−convergence theorems for a class of k-positive linear rates of ideal convergence for approximation operators a note on the statistical approximation properties of the matrix summability and positive linear operators ozlem g local approximation results for sz ́asz-mirakjan type operators a korovkin-type approximation theorem for double sequences approximation theory and functional analysis on time scales some approximation theorems for a general class of prof dr radu p alt anea transilvania university of braÈÂTMov approximation of functions by some types of szasz-mirakjan some approximation results for bernstein-kantorovich approximation by a generalization of the arxiv approximation by kantorovich-szász type operators based on approximation of functions by convexity ams on approximation properties of certain multidimensional approximation properties of rth order generalized
85 citations
TL;DR: In this article, the authors considered the problem of phase retrieval from images obtained using a coherent shift-invariant linear imaging system whose associated transfer function (i.e., the Fourier transform of the complex point spread function) is well approximated by a linear function of spatial frequency.
78 citations
TL;DR: In this paper, a new zig-zag coupled theory was developed for hybrid cross-ply plates with some piezoelectric layers using third-order zigzag approximation for the inplane displacements and sublayer wise piecewise linear approximation for electric potential.
Abstract: A new zig-zag coupled theory is developed for hybrid cross-ply plates with some piezoelectric layers using third-order zig-zag approximation for the inplane displacements and sublayer wise piecewise linear approximation for the electric potential. The theory considers all electric field components and can model open and closed-circuit boundary conditions. The deflection field accounts for the transverse normal strain due to the piezoelectric d 33 coefficient. The displacement field is expressed in terms of five displacement variables (which are the same as in FSDT) and electric potential variables by satisfying exactly the conditions of zero shear stresses at the top and bottom, and their continuity at layer interfaces. The governing equations are derived from the principle of virtual work. Comparison of the Navier solutions for the simply-supported plates with the analytical three-dimensional piezoelasticity solutions establishes that the present efficient zig-zag theory is quite accurate for moderately thick plates.
54 citations
TL;DR: In this article, a general thermal mathematical model for the entire satellite is constructed from a combined conduction and radiation heat transfer equation with environmental heating and cooling as boundary conditions, and the linear approximation and exact formulation for solving this simplified problem, as well as corresponding results shown in graphical form, are also discussed.
Abstract: Thermal analysis is the major engineering work throughout the entire satellite development process, with some crucial stages such as design, test, and ground operations simulation. In the formal design and verification (by test) phases, a general thermal mathematical model for the entire satellite is constructed from a combined conduction and radiation heat transfer equation with environmental heating and cooling as boundary conditions. Some representative numerical schemes with constraints used in satellite thermal analysis, as well as an introduction to the thermal model for the thermal balance test, are presented. However, the general thermal model may be too complicated or inefficient for conceptual design, test monitoring, and ground-operation simulation while developing a satellite. Therefore, simpler governing equations for pure radiation heating and cooling with exact mathematical solutions are developed to fulfill this objective at the expense of analysis accuracy. The linear approximation and exact formulation for solving this simplified problem, as well as the corresponding results shown in graphical form, are also discussed.
54 citations
TL;DR: In this paper, the validity of the tangent linear approximation and of the incremental 4D-Var formulation is evaluated in the operational context and the accuracy of the linear model is assessed with respect to resolution, linearized physics and the length of the assimilation window.
Abstract: The validity of the tangent linear approximation and of the incremental 4D-Var formulation is evaluated in the operational context. In ECMWF's operational system, the linear and adjoint models are run at a lower resolution than the nonlinear model. Furthermore, the physics are simpler in the tangent linear and adjoint than in the nonlinear model. Comparisons are made between the output of the linear model and the finite difference obtained by running the nonlinear model twice, with and without adding the analysis increment. The accuracy of the linear model is assessed with respect to resolution, linearized physics and the length of the assimilation window.
The most striking results are that linearization errors are larger than expected and that large errors appear very early in the assimilation window. It is also shown that higher resolution 4D-Var will require more accurate linear physics than currently available. A modification of the computation of the trajectory around which the problem is linearized is shown to improve the accuracy of the linearization.
The results and diagnostic tools presented should provide guidance for further developments of the incremental 4D-Var, with respect to resolution changes and improvements in linearized physics and dynamics. Copyright © 2004 Royal Meteorological Society
50 citations
TL;DR: Pendry et al. as discussed by the authors showed that the finite-difference time-domain technique suffers from a numerical artifact due to its staggered grid that makes its use in simulations involving backward-wave materials problematic.
Abstract: Backward-wave (BW) materials that have simultaneously negative real parts of their electric permittivity and magnetic permeability can support waves where phase and power propagation occur in opposite directions. These materials were predicted to have many unusual electromagnetic properties, among them amplification of the near-field of a point source, which could lead to the perfect reconstruction of the source field in an image [J. Pendry, Phys. Rev. Lett. vol. 85, pp. 3966, 2000]. Often systems containing BW materials are simulated using the finite-difference time-domain technique. We show that this technique suffers from a numerical artifact due to its staggered grid that makes its use in simulations involving BW materials problematic. The pseudospectral time-domain technique, on the other hand, uses a collocated grid and is free of this artifact. It is also shown that when modeling the dispersive BW material, the linear frequency approximation method introduces error that affects the frequency of vanishing reflection, while the auxiliary differential equation, the Z-transform, and the bilinear frequency approximation method produce vanishing reflection at the correct frequency. The case of vanishing reflection is of particular interest for field reconstruction in imaging applications.
47 citations
17 May 2004
TL;DR: The paper proposes a numerically efficient way of generating spatial correlation matrices for indoor clustered channel models using a uniform linear array approximation to avoid numerical integrals and derives a closed-form expression for the correlation coefficients, assuming a Laplacian angle distribution.
Abstract: The capacity and error rate performance of a multiple-input multiple-output (MIMO) communication system depend strongly on the spatial correlation properties introduced by clustering in the propagation environment. Simulating correlated channels, using, for example, the common correlated Rayleigh fading model, requires numerically complex calculations of the transmit and receive spatial correlation matrices as a function of the cluster size and location. The paper proposes a numerically efficient way of generating these correlation matrices for indoor clustered channel models. The method makes use of a uniform linear array approximation to avoid numerical integrals and derives a closed-form expression for the correlation coefficients, assuming a Laplacian angle distribution. Simulations show that the approximate correlation model exhibits good fit for moderate angle spreads. Complexity calculations show that this approach takes about 1/200 of the time to compute the spatial correlation matrices compared to existing methods.
TL;DR: The Taylor approximation to the n-input constant elasticity of substitution (CES) function is presented and compared to Kmenta's well-known approximation for n = 2 as discussed by the authors.
Abstract: The Taylor approximation to the n-input constant elasticity of substitution (CES) function is presented and compared to Kmenta's well-known approximation for n = 2. The n-input approximation is, as for n = 2, a translog function, but with more complex restrictions on the translog parameters. Bias and consistency of the Taylor approximation to the n-input CES function are discussed, and it is argued that the approximation will only give reliable results for a limited regime of CES parameters and input values. A test of CES structure of the n-input translog function is performed for the fleet of Danish trawlers operating in the North Sea from 1987-99.
TL;DR: By passing to the limit in the finite element approximations, the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained, and strong a priori estimates for the finiteelement solutions are derived.
Abstract: Semidiscrete finite element approximations of a linear fluid-structure interaction problem are studied. First, results concerning a divergence-free weak formulation of the interaction problem are reviewed. Next, semidiscrete finite element approximations are defined, and the existence of finite element solutions is proved with the help of an auxiliary, discretely divergence-free formulation. A discrete inf-sup condition is verified, and the existence of a finite element pressure is established. Strong a priori estimates for the finite element solutions are also derived. Then, by passing to the limit in the finite element approximations, the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained.
TL;DR: Three classes of excitation signals will be used in an optimised measurement strategy, reducing the leakage effects to acceptable levels, allowing to separate the disturbing noise influence from the impact of non-linear contributions, and resulting in the ‘best linear approximation’ of the system.
TL;DR: In this paper, the applicability of total least squares (TLS) algorithms for the estimation of modal parameters in the frequency-domain from input-output Fourier data is studied.
TL;DR: In this paper, the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem is analyzed and the optimal order error estimates for the eigenfunctions when this numerical integration is used are obtained.
Abstract: In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.
TL;DR: The proposed frame-level rate- control method exploits rate-distortion optimization (RDO) to estimate macroblock modes and bitrates for the initial quantization parameter (QP) and outperforms the existing rate-control method.
Abstract: The paper models relations of rate–ρ and QP–ρ, where ρ is defined as the percentage of zero coefficients in a frame. These two models are used for a frame-level rate-control of H.264. A linear approximation scheme is adopted to model the rate–ρ relations for the rate-control. The proposed frame-level rate-control method exploits rate-distortion optimization (RDO) to estimate macroblock modes and bitrates for the initial quantization parameter (QP). An intra-rate model is also designed to determine an initial QP for the intra-frame. In experimental results, peak signal-to-noise ratio, bitrate estimation error, rate-control accuracy in the scene changes, and computational complexity of the proposed method are analyzed for various video sequences. According to the experimental analysis, the proposed method outperforms the existing rate-control method (Joint Video Team of ISO/IEC and ITV-T the Fifth Meeting, JVT-DO69, Geneva, Switzerland, 9–17 October 2002).
Journal Article•
TL;DR: In this article, a modified Born approximation based on the extended Born approximation is proposed for the inversion of large contrast dielectric objects buried in a lossy earth using the idea of backconditioner and lumped-mass approximation.
Abstract: Linear inverse scattering method based on the Born approximation has found wide applications in the on-site detection of buried objects, such as in diffraction tomography. However, the Born approximation becomes invalid when the contrast of targets is high, in which the multiple-scattering effect within the target is more important. To avoid solving the nonlinear inverse scattering problem for large-contrast objects, quasi-linear and modified quasi-linear approximations are proposed based on the extended Born approximation. In this paper, new formulations are derived for the inversion of large-contrast dielectric objects buried in a lossy earth using the idea of backconditioner and lumped-mass approximation. We have shown that the zeroth-order form of such formulations is just the well-known Born approximation, and the first-order form is completely equivalent to the extended Born approximation-based quasi-linear approximation. Hence, high-order approximations are proposed in this paper, which are given in closed forms. Using such approximations, good resolution images can be obtained for large-contrast objects by only solving a linear inverse scattering integral equation. Reconstruction examples show the validity and efficiency of the proposed formulae.
TL;DR: In this article, the authors give a space-time Galerkin finite element discretisation of the quasistatic compressible linear viscoelasticity problem as described by an elliptic partial differential equation with a fading memory Volterra integral.
18 May 2004
TL;DR: In this paper, a nonlinear MIMO system can be replaced by a linear system plus a non-linear noise source, and the optimized measurement strategy is proposed to measure the nonparametric FRF.
Abstract: In this paper it is shown that a nonlinear MIMO system can be replaced by a linear system plus a nonlinear noise source. The optimized measurement strategy is proposed to measure the nonparametric FRF.
07 Jun 2004
TL;DR: In this article, the authors show how to approximate a separable concave minimization problem over a general closed ground set by a single piecewise linear minimization, where the approximation is to arbitrary 1+e precision in optimal cost.
Abstract: We show how to approximate a separable concave minimization problem over a general closed ground set by a single piecewise linear minimization problem. The approximation is to arbitrary 1+e precision in optimal cost. For polyhedral ground sets in \(\mathbb{R}^n_+\) and nondecreasing cost functions, the number of pieces is polynomial in the input size and proportional to 1/log(1+e). For general polyhedra, the number of pieces is polynomial in the input size and the size of the zeroes of the concave objective components.
TL;DR: This paper develops and illustrates methods of self-affine, hierarchical, and correlation analyses of time series and proposes a computationally effective algorithm for decomposition of a time series into a hierarchy of trends at different scales.
Abstract: This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated, and on its base, a computationally effective algorithm is constructed for decomposition of a time series into a hierarchy of trends (local linear approximations) at different scales. The top of the hierarchy is the global linear approximation over the whole observational interval, the bottom is the original time series. Each internal level of the hierarchy corresponds to a piecewise linear approximation of analyzed series. Possible applications of the introduced Multiscale Trend Analysis (MTA) go far beyond the linear interpolation problem: This paper develops and illustrates methods of self-affine, hierarchical, and correlation analyses of time series.
Journal Article•
TL;DR: A formal statistical framework for block cipher attacks based on this technique is developed and explicit and compact gain formulas for generalized versions of Matsui’s Algorithm 1 and Algorithm 2 are derived.
Abstract: In this paper we study the long standing problem of information extraction from multiple linear approximations. We develop a formal statistical framework for block cipher attacks based on this technique and derive explicit and compact gain formulas for generalized versions of Matsui's Algorithm 1 and Algorithm 2. The theoretical framework allows both approaches to be treated in a unified way, and predicts significantly improved attack complexities compared to current linear attacks using a single approximation. In order to substantiate the theoretical claims, we benchmarked the attacks against reduced-round versions of DES and observed a clear reduction of the data and time complexities, in almost perfect correspondence with the predictions. The complexities are reduced by several orders of magnitude for Algorithm 1, and the significant improvement in the case of Algorithm 2 suggests that this approach may outperform the currently best attacks on the full DES algorithm.
07 Nov 2004
TL;DR: This work proposes a technique for optimizing the runtime in statistical timing analysis by budgeting this global error across all nodes in the circuit through piecewise linear approximation and hierarchical quadratic approximation.
Abstract: We propose a technique for optimizing the runtime in statistical timing analysis. Given a global acceptable error budget at the primary output which signifies the difference in the area of the accurate and approximate timing CDFs, we propose a formulation of budgeting this global error across all nodes in the circuit. This node error budget is used to simplify the computation of arrival time CDFs at each node using approximations. This simplification reduces the runtime of statistical timing analysis. We investigate two ways of exploiting this node error budget, firstly through piecewise linear approximation (see ibid., A. Devgan and C. Kashyap, 2003) and secondly though hierarchical quadratic approximation. Experimental results on ISCAS/MCNC benchmarks show that our approach is at most 3 times faster than accurate statistical timing analysis and had a very small error. We also found quadratic piecewise approximation to be more accurate than linear approximation but at lesser gains in runtime.
01 Jan 2004
TL;DR: The Finite Element Method FEM (FEM) as mentioned in this paper is an extensively used tool for solving differential equations that is based on piecewise polynomial approximation, see the Chapters FEM for two-point boundary value problems and Fem for Poisson's equation.
Abstract: Approximating a complicated function to arbitrary accuracy by “simpler” functions is a basic tool of applied mathematics. We have seen that piecewise polynomials are very useful for this purpose, and that is why approximation by piecewise polynomials plays a very important role in several areas of applied mathematics. For example, the Finite Element Method FEM is an extensively used tool for solving differential equations that is based on piecewise polynomial approximation, see the Chapters FEM for two-point boundary value problems and FEM for Poisson’s equation.
TL;DR: In this paper, a new approach to design uniplanar gradient coils for magnetic resonance imaging (MRI) is presented, which involves a constraint cost function between the desired field in a particular region of interest in space and the current-carrying coil plane based on Biot-Savart's integral equation.
Abstract: A new approach to design uniplanar gradient coils for magnetic resonance imaging (MRI) is presented. The theoretical formulation involves a constraint cost function between the desired field in a particular region of interest in space and the current-carrying coil plane based on Biot-Savart's integral equation. An appropriate weight function in conjunction with linear approximation functions allows the transformation of the problem formulation into a linear matrix equation in which its iterative solution yields discrete current elements in terms of magnitude and direction within the prescribed coil plane. These current elements can be synthesized into an overall practical wire configuration by suitably adding individual wire loops. Numerical predictions and practical testing for a Gy gradient coil underscore the success of this approach in terms of achieving a highly linear field while maintaining low parasitic fields. © 2004 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 20B: 17–29, 2004
TL;DR: An L^~-error estimate is established developing a very simple approach based mainly on a discrete L~-stability property with respect to the data for the corresponding discrete coercive problem.
23 May 2004
TL;DR: This paper presents the realization of a scalable architecture, the Negative Logarithmic Function (NLF), for the integer calculation of nonlinear functions and shows how to implement the desired analog logarithm and its reciprocal function with very little logic and a maximizable accuracy.
Abstract: This paper presents the realization of a scalable architecture, the Negative Logarithmic Function (NLF), for the integer calculation of nonlinear functions. It shows how to implement the desired analog logarithm and its reciprocal function with very little logic and a maximizable accuracy. After introducing the NLF module and its properties, we describe the way the continuous function is approached in order to come across the hardware realization. A simple solution is given to reduce the error made by the approximation, as well as the architecture for the reverse transformation. To illustrate the method, examples are given in which the width of the input value has been arbitrarily fixed to 8 bits, whereas the scalable architecture supports every kind of bus width.
01 Jan 2004
TL;DR: In this article, a two-level approximation method (TLA) is proposed for reliability-based design optimization (RBDO), where a reduced second-order approximation is used for better optimisation solution; at the second level a linear approximation was used for faster reliability assessment.
Abstract: In order to model uncertainties and achieve the required reliability, Reliability-Based Design Optimisation (RBDO) has evolved as a dominant design tool. Many methods have been introduced to solve the RBDO problem. However, the computational expense associated with the probabilistic constraint evaluation still limits the applicability of the RBDO to practical engineering problems. In this paper, a Two-Level Approximation method (TLA) is proposed. At the first level, a reduced second order approximation is used for better optimisation solution; at the second level a linear approximation is used for faster reliability assessment. The optimal solution is obtained iteratively. The proposed method is tested on certain numerical examples, and results obtained are compared to evaluate the cost-effectiveness.
18 May 2004
TL;DR: It is shown that in the presence of nonlinear distortions the choice between the two model types will depend on the intended use of the model.
Abstract: The aim of the study presented in this paper is to provide an experimental comparison between best linear approximation models and nonlinear models estimated for systems suffering nonlinear distortions. This is illustrated on a nonlinear mechanical resonating system. Parametric best linear approximation models are estimated from frequency response function measurements using random phase multisines. A full nonlinear model is also estimated for the system. The two types of models are then compared in terms of their performance in simulating the system and also when used as a basis for optimal controller design for the system. It is shown that in the presence of nonlinear distortions the choice between the two model types will depend on the intended use of the model.