Showing papers on "Linear approximation published in 1990"
TL;DR: In this paper, a closed-form solution to the shape-from-shading problem is presented, and an improved method for estimating the illuminant direction is also presented.
Abstract: In many situations the reflectance function of a surface is approximately linear, and there is an effielent closed-form solution to the shape-from-shading problem. When boundary conditions (e.g., edges, singular points) are not available, good estimates of shape may still be extracted by using the assumption of general viewing position. An improved method for estimating the illuminant direction is also presented.
182 citations
TL;DR: In this article, the authors performed experiments on a vorticity equation model on a shallow-water equation model and showed that the results confirmed the results previously obtained, namely that the variational process reconstructs to a satisfactory degree of accuracy the meteorological structures of the flow.
Abstract: Experiments of variational assimilation, similar to those already performed by the authors on a vorticity equation model are performed on a shallow-water equation model. The variational algorithm requires the computation of the gradient of the distance function to be minimized with respect to the model state at the beginning of the assimilation period. As in the previous experiments, this gradient is computed by using the adjoint equations of the model. Northern Hemisphere observations of wind and geopotential, distributed at the 500 mb level over a 24-h time period, are assimilated with a spectral model truncated at degree 21. The results confirm the results previously obtained, namely that the variational process reconstructs to a satisfactory degree of accuracy the meteorological structures of the flow. In addition: (i) Gravity wave noise can be efficiently eliminated by adding an appropriate penalty term to the distance function, and by introducing in the variational process a nonlinear normal mode initialization algorithm. The latter has the effect of improving the numerical conditioning of the variational process. (ii) The quality of forecasts produced from the results of variational assimilation is similar to the quality of shallow-water equation forecasts produced from the results of operational assimilations, which use many more data and more realistic models. Assimilations performed with a model truncated at degree 42 produce similar results. They also show that the numerical efficiency of the variational process, as measured by the number of descent steps necessary to reach convergence, is almost insensitive to the dimension of the model phase space. Finally, study of the variations of the distance function suggests that, as in the case of the vorticity equation, the tangent linear approximation to the model equations is valid in the conditions of data assimilation. DOI: 10.1034/j.1600-0870.1990.t01-4-00004.x
157 citations
TL;DR: The paper presents computational results that were obtained by employing a Rolling Horizon Procedure to simulate the operation of the truckload carrier and indicates the superiority of the new algorithm over other approaches tested.
Abstract: The Stochastic Dynamic Vehicle Allocation problem involves managing a fleet of vehicles over time in an uncertain demand environment to maximize expected total profits. The problem is formulated as a Stochastic Programming problem. A new heuristic algorithm is developed and is contrasted to various deterministic approximations. The paper presents computational results that were obtained by employing a Rolling Horizon Procedure to simulate the operation of the truckload carrier. Results indicate the superiority of the new algorithm over other approaches tested.
151 citations
15 Mar 1990
TL;DR: In this paper, a family of methods is presented for the determination of the adsorption affinity distribution function for a heterogeneous surface from single component adaption data, which is possible to deal with different types of local isotherms and with random and patchwise heterogeneity.
Abstract: A family of methods is presented for the determination of the adsorption affinity distribution function for a heterogeneous surface from single component adsorption data. It is possible to deal with different types of local isotherms and with random and patchwise heterogeneity. The general concept is that an approximation of the local isotherm is used to solve the integral adsorption equation analytically for the distribution function without making a priori assumptions about the distribution. The method is worked out for FFG type equations as local isotherm with an interaction parameter incorporated. Examples are given for the Langmuir local isotherm. The simplest member of this family of local isotherm approximations (LIA) is the step function (STEP), known as the condensation approximation (CA). The first order affinity spectrum (AS1) strongly resembles the CA distribution. Both methods result in general in a too wide affinity distribution. An alternative is the use of a linear approximation (LINA) of the local isotherm. These LINA methods cause a widening and an asymmetric deformation of the true distribution. The asymptotically correct condensation approximation (ACCA) is a member of this group. A substantially better approximation is achieved by considering the local isotherm and its approximations on a logarithmic concentration (or mole fraction) scale (LOGA). The distributions obtained with the Rudzinski Jagiello (RJ) method and the second order affinity spectrum (AS2) method can be interpreted as members of the LOGA group. Parameter optimization in the LOGA case has resulted in two other solutions which are better approximations than the RJ and AS2 method.
83 citations
TL;DR: In this article, the results of direction-of-arrival estimation by eigenvalue analysis are extended to derive a recursive procedure based on a matrix quadratic equation, which is used to provide updated target positions.
Abstract: The use of the output of an array of sensors to track multiple independently moving targets is reported. The output of each sensor in the array is the sum of signals received from each of the targets. The results of direction-of-arrival estimation by eigenvalue analysis are extended to derive a recursive procedure based on a matrix quadratic equation. The solution of this matrix quadratic equation is used to provide updated target positions. A linear approximation method for estimating the solution of the matrix equation is presented. The algorithm is demonstrated by the simulated tracking of two targets. The main advantage of the algorithm is that a closed-form solution for updating the target angle estimates has been obtained. Also, its application is straightforward, and the data association problem due to uncertainty in the origin of the measurements is avoided. However, it requires the inversion of an N*N as well as other linear operations, so that the computational burden becomes substantial as N becomes very large. >
78 citations
04 Dec 1990
TL;DR: The key idea is that the local spatial structure of optical flow, with the exception of surface boundaries, is usually rather coherent and can thus be appropriately approximated by a linear vector field.
Abstract: A method is presented for the recovery of optical flow. The key idea is that the local spatial structure of optical flow, with the exception of surface boundaries, is usually rather coherent and can thus be appropriately approximated by a linear vector field. According to the proposed method, the optical flow components and their first order spatial derivatives are computed at the central points of rather large and overlapping patches which cover the image plane as the solution to a highly overconstrained system of linear algebraic equations. The equations, which are solved through the use of standard least mean square techniques, are derived from the assumptions that the changing image brightness is stationary everywhere over time and that optical flow is, locally, a linear vector field. The method has been tested on many sequences of synthetic and real images and the obtained optical flow has been used to estimate three-dimensional motion parameters with very good results. >
77 citations
TL;DR: In this article, a bilinear square-root approximation with complex coefficients is introduced that accommodates all mode types and leads to stable numerical solutions for two-dimensional elastic waveguides.
Abstract: One‐way or parabolic wave equations for time‐harmonic propagation in two‐dimensional elastic waveguides are considered. It is shown that the direct application of a rational linear approximation with real coefficients to the elastic wave propagation case results in exponential growth in the numerical solutions. Elementary analysis demonstrates that this kind of approximation does not treat properly the modes with complex wavenumber which can exist in elastic waveguides. A new bilinear square‐root approximation with complex coefficients is introduced that accommodates all mode types and leads to stable numerical solutions. In the case of thick elastic layers (such as sea‐bottom sediments), this new approximation gives accurate total field prediction. When thin elastic layers (such as ice on the sea surface) are present, however, the method introduces excessive damping to modes with wavenumbers significantly different from a reference wavenumber.
65 citations
62 citations
TL;DR: The linear RC delay modeling technique is used to model the timing delays in CMOS circuit empirically to be simplified to a two-dimensional model which estimates the delay of a CMOS subcircuit in terms of the generic RC delay ad the rise/fall time of the input transition.
Abstract: The linear RC delay modeling technique is used to model the timing delays in CMOS circuit empirically. The empirical model, a multidimensional function of various circuit and device parameters, is shown to be simplified to a two-dimensional model which estimates the delay of a CMOS subcircuit in terms of the generic RC delay ad the rise/fall time of the input transition. Accuracy limitations of the linear RC delay model are investigated; namely, (i) the single-time-constant approximation on the multiple-pole network function; (ii) the linear resistance approximation on the nonlinear MOSFET characteristic; and (iii) the step-input waveform assumption. These accuracy problems are handled by: (1) presenting an accuracy measure of the simpler model and an option for using the more accurate two-time-constant model; (2) exploiting the nonlinear body effect in the transmission gate to improve the linear resistance characterization; and (3) using the piecewise-linear characterization on the input rise/fall time effect. The model has been installed in an experimental simulator and tested for various circuits. Comparisons are made with SPICE to validate the model reliability. >
44 citations
05 Dec 1990
TL;DR: In this article, a set of extended quadratic controller normal forms of linearly controllable systems with single input is given, and it is proved that, given a nonlinear system, there exists a dynamic feedback so that the extended system has a linear approximation which is accurate to the second or higher degree.
Abstract: A set of extended quadratic controller normal forms of linearly controllable systems with single input is given. These normal forms are considered as the extension of the form due to P. Brunovsky (1970) to the nonlinear systems. It is proved that, given a nonlinear system, there exists a dynamic feedback so that the extended system has a linear approximation which is accurate to the second or higher degree. All the results are restricted to the single-input nonlinear systems. The idea of finding quadratic normal forms and extending the state space is also successfully used in the problem of finding nonlinear observers. >
01 Jan 1990
TL;DR: This book discusses the modeling of MOS Devices, Green's Function for Stratified Media, and the Modeling of a Short-channel MOSFET below Threshold using the Fourier Integral Evaluation.
Abstract: 1. Introduction.- 1.1 Modeling of MOS Devices.- 1.2 Parasitic Models.- 1.3 Background from Algebra.- 1.4 Background from Analysis.- 1.5 Overview of the Book.- 2. Boundary Value Problems in VLSI Modeling.- 2.1 Field Equations.- 2.2 Integral Equations: the MOSFET Case.- 2.3 Integral Equations: Parasitic Capacitance.- 3. Green's Function for Stratified Media.- 3.1 Definition.- 3.2 The Bounded Multilevel Dielectric Problem.- 3.3 The Unbounded Multilevel Dielectric Problem.- 4. Galerkin Boundary Finite Elements.- 4.1 Element and Local Shape Function.- 4.2 An Optimal Solution.- 4.3 Reduction Using Constraints.- 4.4 Evaluation of Green's Function Integrals.- 4.5 Determination of the Number of Terms Required for Green's Function.- 4.6 Results and Comparisons.- 5. Point Collocation and Further Simplifications.- 5.1 Point Collocation.- 5.2 Further Reduction of Point-Collocation Integrals.- 5.3 The Capacitance Matrix.- 6. Reduced Models.- 6.1 Preliminaries.- 6.2 The Generalized Schur Algorithm.- 6.3 Approximation Theory and Error Analysis.- 6.4 Architectures.- 7. Hierarchical Reduced Models.- 7.1 Two Dimensional Ordering.- 7.2 Hierarchical Approximants.- 7.3 The Sparse Inverse Approximation.- 8. On the Modeling of a Short-channel MOSFET below Threshold.- 8.1 Analytical Solution of the Poisson Equation.- 8.2 Boundary Conditions.- 8.3 Discussion.- 9. Parasitic Capacitances and their Linear Approximation.- 9.1 Parallel Conductors.- 9.2 Corners.- 9.3 Crossing Strips.- 9.4 Combination of Corner and Crossing Strips.- 10. Interconnection Resistances.- 10.1 Introduction.- 10.2 Finite Element Method.- 10.3 The Boundary Finite Element Method.- 11. Hybrid Finite Elements.- 11.1 Introduction.- 11.2 Direct Hybrid Field Modeling.- 11.3 Extension to the Poisson Case.- 11.4 Using a Scattered Field.- 12. Appendices.- 12.1 Appendix 3.1: Solution of Equation (3.8).- 12.2 Appendix 3.2: Fourier Integral Evaluation.- 12.3 Appendix 4.1: Evaluation of Singular Integrals.- 12.4 Appendix 4.2: Derivation of (4.41).- 12.5 Appendix A.5.
TL;DR: In this paper, two tapered beam finite elements have been developed for rotor bearing analysis, and a linear approximation is used for the geometrical properties yielding closed form expressions for the element matrices.
TL;DR: In this paper, the authors investigate three different approximation methods in the context of a neoclassical model with a production tax and compare their solutions with solutions obtained from a discrete state space solution to the Euler equations of the model.
Abstract: Real business cycle models have recently been applied to settings in which equilibria are suboptimal. In most models the solutions are approximated using some type of linearization with little attention being given to the accuracy of the approximation. In this paper we investigate three different approximation methods in the context of a neoclassical model with a production tax and compare their solutions with solutions obtained from a discrete state space solution to the Euler equations of the model.
TL;DR: In this paper, a metric-torsion gauge theory of line defects is developed and a Lagrangian containing curvature terms up to second power has constant-curvature solutions.
Abstract: Basic points underlying the geometrization of continuum defects are discussed. Following an analogy with gravitational gauge theories, a metric-torsion gauge theory of continuum line defects is developed. Gauge-invariant action integrals are constructed and their equations of motion are obtained. A Lagrangian containing curvature terms up to second power has constant-curvature solutions. In linear approximation these solutions correspond to line defects which form closed loops separately.
TL;DR: In this paper, the authors examine properties of strongly unique best approximation in terms of extremal functionals in an abstract normed linear space using some new or modified tools (e.g., the shadow of a set, strongly tangent sets, I-sets) and express criteria of strong uniqueness both in linear and nonlinear approximation.
Abstract: In the paper we examine properties of strongly unique best approximation in terms of extremal functionals in an abstract normed linear space. Using some new or modified tools (e.g., the shadow of a set, strongly tangent sets, I-sets) we express criteria of strong uniqueness both in linear and nonlinear approximation. Some further remarks are contributed to the discussion on Poreda's problem concerning the behavior of the strong unicity constants and a detailed description of properties of the tangent cone of Dubovitsky-Milyutin is given.
TL;DR: In this article, a general method was proposed to solve in the linear approximation the fourth-order gravitational equations, which stem from Lagrangians, and the metric of a static spherically symmetric body and a straight infinitely thin cosmic string were given.
Abstract: A general method is proposed to solve in the linear approximation the fourth-order gravitational equations, which stem from Lagrangians The metric of a static spherically symmetric body and the metric of a straight infinitely thin cosmic string are given.
01 Jan 1990
TL;DR: An approximation method is presented for probabilistic inference with continuous random variables, based on the Gaussian influence diagram, that iterates over linear approximations to the inference problem.
Abstract: An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are “second order” probabilities. The approximation, based on the Gaussian influence diagram, iterates over linear approximations to the inference problem.
TL;DR: In this article, an improved finite element method (FEM) was applied to calculate the thrust of an automotive solenoid valve which operates in the high flux density region near saturation, and the calculated values obtained from the improved FEM were in better agreement with the experimental values than the usual linear approximation using the Maxwell tensor.
Abstract: A method is proposed to calculate the thrust of a magnetic actuator that operates in the nonlinear magnetic region. The magnetic force expression of the Maxwell stress tensor is expanded to cover magnetic saturation by using a successive approximation of the surface force on the magnetizing curve. The resulting improved finite-element method (FEM) approximation is applied to calculate the thrust of an automotive solenoid valve which operates in the high flux density region near saturation. The calculated values obtained from the improved FEM are in better agreement with the experimental values than the usual linear approximation using the Maxwell stress tensor. >
TL;DR: In this paper, a finite dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions are presented for optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system.
Abstract: Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.
01 Apr 1990
TL;DR: A method is presented for determining the unknown degree and system function of any 2-D discrete linear shift-invariant system characterized by a2-D impulse response array, i.e., the coefficients of the formal double power series that are obtained by expanding a rational transfer function.
Abstract: A method is presented for determining the unknown degree and system function of any 2-D discrete linear shift-invariant system characterized by a 2-D impulse response array, i.e., the coefficients of the formal double power series that are obtained by expanding a rational transfer function. Problems of 2-D Pade approximation and 2-D system reduction can be solved by the same method by making a reasonable assumption in the context of 2-D linear systems theory. The method is based on a 2-D extension of the Berlekamp-Massey algorithm for synthesis of linear feedback shift registers. It gives a novel approach to identification and approximation of 2-D linear systems and is comparable in efficiency with other methods for 2-D rational approximation based on the block Toeplitz and block Hankel matrices. >
TL;DR: A new technique is presented for the analysis ofNon-linear stochastic systems in which they are represented by a series of non-linearly coupled linear systems and a measure of the error and second-order correction terms for the linear approximation is obtained.
Abstract: A new technique is presented for the analysis of non-linear stochastic systems in which they are represented by a series of non-linearly coupled linear systems. Considerable insight is gained in the approximation of non-linear stochastic systems by linear systems and in the use of describing functions. A measure of the error and second-order correction terms for the linear approximation are obtained. The analysis is extended to the non-zero mean case.
TL;DR: In this article, a linear stationary wave model is used to diagnose the causes of stationary waves in integrations of a general circulation model (GCM) and to indicate the sources of differences between the stationary waves of separate integrations.
Abstract: A linear stationary wave model is used to diagnose the causes of stationary waves in integrations of a general circulation model (GCM) and to indicate the sources of differences between the stationary waves of separate integrations. The GCM generates solutions to the equations of motion. The linear model, constructed to be as similar as possible in structure to the GCM, is employed in various attempts to approximate and understand the time averages of the GCM solutions. When GCM values for internal dissipation time constants are used in the linear model, significant differences between the linear model and GCM solutions are found. These differences can be interpreted as errors due to the linear approximation. The linear simulation is improved somewhat by enhancing the scale selective horizontal diffusion. The linear model with enhanced dissipation is used to simulate the differences between the stationary waves of two consecutive months of a GCM integration. Transient forcing turns out to be the ...
TL;DR: In this article, a method to approximate distributed parameter systems by finite dimensional linear systems is presented, where the impulse and step responses of the original systems are well approximated by using the singular value decomposition.
Abstract: A new method to approximate distributed parameter systems, which normally have an infinite dimension, by finite dimensional linear systems is presented. The impulse and step responses of the original systems are well approximated by using the singular value decomposition. A telegraph cable example is presented to demonstrate the usefulness of the method.
05 Dec 1990
TL;DR: In this paper, a unified approach for rational approximations of possibly unstable linear infinite-dimensional systems is proposed, where the system transfer function is assumed to be continuous on the imaginary axis with finitely many poles in the open right half plane, and a procedure is developed for constructing a sequence of finite-dimensional approximants which converges to the true model in the L/sub infinity / norm.
Abstract: The approximation of possibly unstable linear infinite-dimensional systems is studied. The system transfer function is assumed to be continuous on the imaginary axis with finitely many poles in the open right half plane. A unified approach is proposed for rational approximations of such infinite-dimensional systems. Under a certain mild frequency domain condition, a procedure is developed for constructing a sequence of finite-dimensional approximants which converges to the true model in the L/sub infinity / norm. It is noted that the proposed technique uses only the fast Fourier transform and the singular value decomposition algorithms for obtaining the approximations. Some examples are included to illustrate the proposed method. >
01 May 1990
TL;DR: In this paper, two gradient adaptive lattice (GAL) algorithms that have been simplified by replacing multipliers and dividers with shifting operations using power-of-two quantization are presented and analyzed.
Abstract: Two gradient adaptive lattice (GAL) algorithms that have been simplified by replacing multipliers and dividers with shifting operations using power-of-two quantization are presented and analyzed. A convergence model is developed for each algorithm, from which the convergence of the mean of the filter coefficients is analyzed. An expression for the asymptotic variance of the filter coefficients of the different algorithms is developed. Both an exact analysis under a Gaussian input assumption and an analysis using a linear approximation of the power-or-two quantizer are compared to simulation results. >
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TL;DR: In this article, the authors investigate three different approximation methods in the context of a neoclassical model with a production tax and compare their solutions with solutions obtained from a discrete state space solution to the Euler equations of the model.
Abstract: Real business cycle models have recently been applied to settings in which equilibria are suboptimal. In most models the solutions are approximated using some type of linearization with little attention being given to the accuracy of the approximation. In this paper we investigate three different approximation methods in the context of a neoclassical model with a production tax and compare their solutions with solutions obtained from a discrete state space solution to the Euler equations of the model.
01 Feb 1990-Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering
TL;DR: A flexible method for Computer Aided Design (CAD) of electromagnetic devices has been obtained based on successive linear approximation of the functions defining the problem using the Finite Element Method.
Abstract: A new method of designing electromagnetic devices is presented in this paper. As a result of applying a very effective algorithm for non‐linear minimax optimization, a flexible method for Computer Aided Design (CAD) of electromagnetic devices has been obtained. The algorithm is based on successive linear approximation of the functions defining the problem. In each iteration step those functions are computed with the aid of the Finite Element Method (FEM). The resulting linear sub‐problems are solved in the minimax sense subject to the linear equality and inequality constraints. The application of the new method for the design of two different examples are presented. The first example is a classical case of shape designing with the aid of the independent nodes movement (INM) method. In the second example the applied equality constraints added to INM have reduced the problem to the optimal location. In both cases the method proved its flexibility and usefulness in CAD.
TL;DR: In this article, a non-linear programming problem with equality constraints is considered, and iterative penalty methods using the linearization approach are proposed to solve it, where the equality constraint is considered.
Abstract: A non-linear programming problem with equality constraints is considered. Iterative penalty methods using the linearization approach are proposed to solve it.