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Showing papers on "Linear approximation published in 1985"


Journal ArticleDOI
TL;DR: In this article, the authors introduce arbitrary frequency weighting into the optimal Hankel-norm approximation problem for scalar, finite-dimensional, linear, time-invariant systems.

150 citations


Journal ArticleDOI
TL;DR: In this article, necessary and sufficient conditions for affine nonlinear systems to be globally feedback equivalent to a controllable linear system over an open subset V of Rn are presented, when V equals Rn.
Abstract: This note presents necessary conditions and sufficient conditions for an affine nonlinear system to be globally feedback equivalent to a controllable linear system over an open subset V of Rn. When V equals Rn, necessary and sufficient conditions are obtained.

85 citations


Journal ArticleDOI
TL;DR: In this article, a new formulation of the direct boundary element method is presented for modelling structural discontinuities, such as geological joints and faults, in heterogeneous rock, where the rock surrounding a discotinuity is assumed to be linear elastic and, for the purpose of modelling, is divided into regions of homogeneous material, with adjacent regions separated by interfaces.

39 citations



Journal ArticleDOI
TL;DR: In this paper, the authors examined the parameter effects curvature measure proposed by Bates and Watts (1980) for a growth model and the Fieller-Creasy problem and found that the agreement between the regions is good despite high curvature.
Abstract: The parameter-effects curvature measure proposed by Bates and Watts (1980) is examined for a growth model and the Fieller-Creasy problem. Exact confidence regions are constructed and compared to linear approximation regions. For the growth model the agreement between the regions is good despite high curvature. In the Fieller—Creasy problem it is shown that the agreement can be quite poor despite low curvature.

33 citations


01 Jan 1985
TL;DR: The PARTAN variant of thelinear approximation method is adapted for solving the network equilibrium problem and its computational efficiency on small and large scale problems is compared to that of the linear approximation method.
Abstract: The PARTAN variant of the linear approximation method is adapted for solving the network equilibrium problem. A simple and efficient algorithm is stated. Its properties are analyzed by using algebraic and geometric approaches. Its computational efficiency on small and large scale problems is compared to that of the linear approximation method.

26 citations



Journal ArticleDOI
TL;DR: A data reduction algorithm suitable for realtime processing is presented, based on the notion that to interpolate a curve efficiently, few points should be placed where the radius of curvature is large, but many where it is small.
Abstract: A data reduction algorithm suitable for realtime processing is presented, based on the notion that to interpolate a curve efficiently, few points should be placed where the radius of curvature is large, but many where it is small. The algorithm estimates the radius of curvature from numerical data.

19 citations


Journal ArticleDOI
TL;DR: In this paper, an algorithm for solving the field equation of the Robinson-Trautman metrics is presented, in the linear approximation, to the line elements which evolve from an axially symmetric initial surface.
Abstract: An algorithm is presented for solving, by a power expansion, the field equation of the Robinson-Trautman metrics It is applied, in the linear approximation, to the line elements which evolve from an axially symmetric initial surface The special case of the ellipsoid of revolution is explicitly treated

9 citations


Journal ArticleDOI
TL;DR: The study describes a sequential iterative modelling process for a complex water resource system where two types of analytical models are used to find a reasonably small set of possible systems optimal design alternatives for acomplex river basin.
Abstract: The study describes a sequential iterative modelling process for a complex water resource system. Two types of analytical models are used to find a reasonably small set of possible systems optimal design alternatives for a complex river basin. These models are a linear programming deterministic continuous (lpdc) model and a linear programing deterministic discontinous (lpdd) model. Linear programing has been used with linear approximation of the nonlinear functions. A simulation program has been developed which continues screening on the basis of the information obtained from the linear programing model. The models are developed in the context of analysis of the Narmada river, a large river basin in India, for which in the first instance alternative combinations and capacities of six major dams have to be decided.

8 citations



Journal ArticleDOI
TL;DR: In this paper, the authors discuss an approximating procedure which is often used in the analysis of damped linear dynamical systems arising in engineering, and discuss an approximation procedure that is used in their work.
Abstract: This paper discusses an approximating procedure which is often used in the analysis of damped linear dynamical systems arising in engineering.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the asymptotic behavior of localized two-dimensional perturbations of the surface of a shear discontinuity separating two homogeneous steady flows of ideal incompressible fluid.
Abstract: The asymptotic behavior of localized two-dimensional perturbations of the surface of a shear discontinuity separating two homogeneous steady flows of ideal incompressible fluid is studied in the linear approximation. The effect of surface tension and gravity forces is taken into account. Mathematically the problem reduces to the investigation by the method of steepest descent of the asymptotic behavior of a double integral for various values of parameters which are the components of the group velocity vector. In this problem the principal difficulty is to find the two-dimensional steepest descent contour in the space of two complex variables that determines which of the various saddle points gives the asymptotic form. First, for the Fourier component with respect to one of the variables with allowance for all the saddle points we find an asymptotic form which parametrically depends on the second variable. The choice of the second variable makes it possible to prove analytically that in the absence of gravity the asymptotic behavior of the growing perturbations is determined by a single saddle point in the plane of that variable. In this way it is possible to justify the authors' previous conclusions [1] concerning the shape of the boundary L of the region D in the group velocity plane occupied by growing perturbations. In the presence of gravity the growth rates of perturbations corresponding to different group velocities are found numerically and the region D occupied by the growing perturbations is indicated.

Journal ArticleDOI
B Wood1
TL;DR: In this article, the order of uniform approximation for linear combinations due to May and Rathore of Baskakov-type operators and recent methods of Pethe is studied for linear combination.

Proceedings ArticleDOI
19 Jun 1985
TL;DR: The focus of the work is on the asymptotic approximatin of the linear system with weak couplings and finite-state Markov processes containing rare transitions.
Abstract: : This paper reports on recent work on time scale decomposition and aggregation of large-scale linear systems containing weak couplings and finite-state Markov processes containing rare transitions. This work builds on that of Coderch, et. al.. The focus of the work is on the asymptotic approximatin of the linear system. (Author)

Proceedings ArticleDOI
01 Dec 1985
TL;DR: In this article, the problem of finding a best approximant of given order, in the l 2 sense, of a given (possibly non rational) discrete linear constant stable system is dealt with.
Abstract: This paper deals with the problem of finding a best approximant of given order, in the l2 sense, of a given (possibly non rational) discrete linear constant stable system. Under generic conditions on the approximant, we give an equation satisfied by the critical points of the distance function.




Journal ArticleDOI
TL;DR: In this article, it was shown that the spin-1 massless field vanishes in the linear approximation for the extended metric tensor, which is a function of an internal vectorya(x).
Abstract: An extended “metric” tensor that is a function of an internal vectorya(x) leads to a spin-1 massless field of gravitational origin. It is shown that this new field vanishes in the linear approximation for the extended “metric.”

Proceedings ArticleDOI
01 Dec 1985
TL;DR: In this paper, a nonlinear adaptive controller is constructed based on a combination of a pole placement design method with a piecewise-polynomial approximation of a titration function, coefficients of which are estimated from pH measurements.
Abstract: Physical inspection leads to the modelling of a pH-reactor by a linear, dynamic flow and mixing process followed by a static nonlinearity. A pH-process very difficult to control is simulated for testing different kinds of adaptive algorithms. In one algorithm, the flow and mixing model is considered known. The nonlinear adaptive controller is constructed based on a combination of a pole placement design method with a piecewise-polynomial approximation of a titration function, the coefficients of which are estimated from pH measurements. The other algorithm uses an inverse overall process model obtained by combination of the flow and mixing model with a piecewise-polynomial approximation of the titration curve. This model is applied to the development of a nonlinear controller based on the model reference adaptive technique. Both methods are applied for tracking a given pH-variable and for regulation. The effectiveness of linear and nonlinear adaptive controllers, obtained using the linear or nonlinear approximation of the titration curve, respectively, are examined and compared for different process solutions and different applications.

Journal ArticleDOI
TL;DR: In this article, an analytical model for the natural circulation in a solar fluid heater is presented for the unsteady state by the application of the conservation laws of mass, momentum and energy to a fluid element of a volume equal to the product of the fluid duct cross-sectional area and an elementary length along the circulation loop.

Journal ArticleDOI
TL;DR: This paper showed that most of the Bera and Byron (1983) results are valid using exact sampling distributions, but show how powers can be calculated easily to compare the two alternative tests.

Posted Content
TL;DR: The authors showed that most of the Bera and Byron (1983) results are valid using exact sampling distributions, but show how powers can be calculated easily to compare the two alternative tests.
Abstract: Abstract In this paper we demonstrate that most of the Bera and Byron (1983) results are valid utilising exact sampling distributions, but show how powers can be calculated easily to compare the two alternative tests.

Book ChapterDOI
16 Sep 1985

Journal ArticleDOI
TL;DR: In this paper, the Schrodinger equation was used to obtain the propagation of nonlinear modulations of a symmetric harmonic mode over a plane magnetic layer in an incompressible fluid.
Abstract: The special features of the distribution of the magnetic field in the photosphere of the Sun and the experimental discovery of waves which propagate along magnetic tubes in the solar atmosphere have brought about the publication recently of a large number of articles which study the wave-conducting properties of media with a magnetic structure. One of the simplest cases was that of a plane magnetic layer, which was studied in detail in the linear approximation [1–3]. Starting from the dispersion properties of such a structure, [4] indicates the possibility of the existence in it of solitons in the approximation of waves of low amplitude which are long in relation to the layer. The present study has used the method of different-scale expansions to obtain the Schrodinger equation describing the propagation of nonlinear modulations of a symmetric harmonic mode over a plane magnetic layer in an incompressible fluid. A similar equation has been deduced, for example, for waves in water [5–9].

Proceedings ArticleDOI
06 Nov 1985
TL;DR: In this paper, the second-order modes of a dynamical system with an internal low rank projection are shown to be bounded from above by the second order modes of the system without the internal projection.
Abstract: Internal projections are used to approximate static linear systems The results are used trs (i) interpret the Kalman experiment and the Ho-Kalman algoritom for identifying finite dimensional linear systems, (ii) derive low rank digital filters with minimum round-of noise variance, and (iii) obtain low rank dynamical systems which approximate finite or infinite rank dynamical systems The second-order modes of a static or dynamical system arise as the natural modes to edit in any rank reduction scheme These modes are invariant to internal structure, so questions of structure play no role in rank reduction until internal constraints are applied and internal noise is considered The second-order modes of a dynamical system with an internal low rank projection are shown to be bounded from above by the second-order modes of the dynamical system without the internal projection This fundamental theorem provides the basis for answering a variety of questions about approximation errors

Journal ArticleDOI
TL;DR: Programs for discrete linear minimax approximation (preferably weighted) can be used to do minimax linear minimAX approximation with Lagrange-type interpolation on infinite compact sets.
Abstract: Programs for discrete linear minimax approximation (preferably weighted) can be used to do minimax linear minimax approximation with Lagrange-type interpolation on infinite compact sets.

Journal ArticleDOI
TL;DR: In this article, the existence of central configurations consisting of a point body, a homogeneous sphere and some drops of homogeneous ideal fluid has been proved by using the virial method.
Abstract: This paper deals with the investigation of central configurations consisting of a point body, a homogeneous sphere and some drops of homogeneous ideal fluid. The existence of such central configurations, as well as the stability of the drops in linear approximation, has been proved by using the virial method (Chandrasekhar, 1969).

Proceedings ArticleDOI
01 Jan 1985
TL;DR: In this paper, a factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays.
Abstract: A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.