Showing papers on "Piecewise linear function published in 1985"
277 citations
TL;DR: In this article, a simple schema simple for determining the gradients a partir de l'approximation a elements finis triangulaires lineaire par morceaux de la solution d'un probleme elliptique du second ordre.
Abstract: On justifie l'utilisation d'un schema simple pour determiner les gradients a partir de l'approximation a elements finis triangulaires lineaire par morceaux de la solution d'un probleme elliptique du second ordre. Le gradient obtenu est une estimation superconvergente du vrai gradient
93 citations
TL;DR: In this paper, the problem of simultaneously determining the optimal price policy and production rate over a given planning horizon is addressed by using optimal control theory, and the solution method is a phase portrait analysis providing insight into the optimal pricing and production policies as well as resulting inventory paths.
87 citations
TL;DR: For the heat equation in two space dimensions, this article considered semidiscrete and totally discrete variants of the lumped mass modification of the standard Galerkin method, using piecewise linear approximating functions.
Abstract: For the heat equation in two space dimensions we consider semidiscrete and totally discrete variants of the lumped mass modification of the standard Galerkin method, using piecewise linear approximating functions, and demonstrate error estimates of optimal order in L2 and of almost optimal order in L∞
61 citations
01 Jan 1985
TL;DR: In this paper, the authors present a method to induce coincidence between one map and another, regardless of their respective projections, by transforming the map to a rubber sheet stretched to coincide with a stable base map at an average of 15 control points.
Abstract: We present a computationally simple and inexpensive method to induce coincidence between one map and another, regardless of their respective projections. We imagine the map to be transformed on a rubber sheet stretched to coincide with a stable base map at an average of 15 control points; for more precise coincidence, we add more control points. We compute triangles on the rubber-sheet map, using control points as vertices, and with a procedure called piecewise linear homeomorphism, map these triangles linearly onto corresponding triangles on the stable map.
56 citations
TL;DR: The rectangular influence graph is presented as an extension of the relative neighborhood graph (RNG) and it is shown that the RIG is a superset of the Gabriel graph with respect to any Minkowski metric.
52 citations
TL;DR: An extremely efficient breakpoint-hopping algorithm is presented for tracing the driving-point and transfer characteristics of any nonlinear circuit made of linear (possibly multi-terminal) resistors, dc independent sources, linear controlled sources and 2-Terminal nonlinear resistors described by piecewise-linear \upsilon - i characteristics.
Abstract: An extremely efficient breakpoint-hopping algorithm is presented for tracing the driving-point and transfer characteristics of any nonlinear circuit made of linear (possibly multi-terminal) resistors, dc independent sources, linear controlled sources (all 4 types) and 2-terminal nonlinear resistors described by piecewise-linear \upsilon - i characteristics. Most resistive nonlinear electronic circuits can be realistically modeled by such circuits. The algorithm can trace not only violently nonlinear (with sharp turning points) and multivalued characteristics, but also characteristics composed of several disconnected branches, provided one point in each branch is given. The remarkable computational efficiency of the breakpoint-hopping algorithm is due to two key properties built into the algorithm: 1) the circuit equation is formulated into a special form; namely, a canonical piecewise-linear equation with a lattice structure. 2) the algorithm finds only the breakpoints and possibly one point on each end (unbounded) segment via explicit formulas (hence no convergence problem). These data points represent the minimal amount of information needed to specify a piecewise-linear characteristic uniquely.
40 citations
TL;DR: The sufficient conditions for chaotic behavior in piecewise-linear sampled-data control systems by applying Shiraiwa-Kurata's theorem are discussed and two types of transition from a fixed point to a chaotic attractor are studied by numerical simulation.
Abstract: This paper discusses the sufficient conditions for chaotic behavior in piecewise-linear sampled-data control systems by applying Shiraiwa-Kurata's theorem. First, it is shown that a discrete-time system with a piecewise-linear element is chaotic if the lower-dimensional system induced from the original system has a snapback repeller. Next, this result is applied to a piecewise-linear sampled-data control system. Finally, the chaotic region for a two-dimensional sampled-data control system with a dead zone element is studied, and two types of transition from a fixed point to a chaotic attractor are studied by numerical simulation.
28 citations
TL;DR: In this article, the applicability of switched-capacitor (SC) components to the design of nonlinear networks is extensively discussed, and the design methods to be proposed are fully compatible with general synthesis methods for nonlinear n -ports.
Abstract: The applicability of switched-capacitor (SC) components to the design of nonlinear networks is extensively discussed in this paper. The main objective is to show that SC's can be efficiently used for designing nonlinear networks. Moreover, the design methods to be proposed here are fully compatible with general synthesis methods for nonlinear n -ports. Different circuit alternatives are given and their potentials are evaluated.
21 citations
01 Jan 1985
TL;DR: In this article, the authors consider four equivalent methods to linearize separable convex piecewise linear programming problems, and show that the exact relationships among them can be established through the application of the decomposition principle of Dantzig and Wolfe.
Abstract: This paper considers four equivalent methods to linearize separable convex piecewise linear programming problems. These methods lead to different linear programming formulations which are necessarily equivalent in the sense that they imply the same optimal solutions. It is shown that the exact relationships among them can be established through the application of the decomposition principle of Dantzig and Wolfe.
20 citations
TL;DR: In this paper, the errors in objective analysis methods that are based on corrections to first-guess fields are considered and an expression that gives a decomposition of an error into three independent components is derived.
Abstract: The errors in objective analysis methods that are based on corrections to first-guess fields are considered. An expression that gives a decomposition of an error into three independent components is derived. To test the magnitudes of the contributions of each component, a series of computer simulations was conducted. The grid-to-observation-point interpolation schemes considered ranged from simple piecewise linear functions to highly accurate spline functions. The observation-to-grid interpolation methods considered included most of those in present meteorological use, such as optimum interpolation and successive corrections, as well as proposed schemes such as thin plate splines, and several variations of these schemes. The results include an analysis of cost versus skill; this information is summarized in plots for most combinations. The degradation in performance due to inexact parameter specification in statistical observation-to-grid interpolation schemes is addressed. The efficacy of the me...
TL;DR: In this paper, the theory of Poincare halfmaps induced by the flow of a three-dimensional linear saddle-focus is developed, which leads for each halfmap to an implicit scalar equation plus a side condition.
Abstract: A piecewise-linear nerve conduction equation is investigated further. The theory of Poincare halfmaps induced by the flow of a three-dimensional linear saddle-focus is developed. Using a description of the dynamical system in diagonalized coordinates, a canonical formulation of two-dimensional halfmaps is found. This leads for each halfmap to an implicit scalar equation plus a side condition. The effect of the halfmaps on different types of invariant curves occurring is investigated. Thereby the capacity of the halfmaps to separate adjacent points (such that the images acquire a finite distance) is shown. Two of three possible mechanisms for separating points are investigated in detail. The regions in the canonical parameter space where the different separating mechanisms appear are indicated analytically. The possible appearance of chaotic solutions, at least in the neighborhood of homoclinic trajectories in state space, is demonstrated. The underlying separation mechanism is present also in regions of state space far from a homoclinic orbit.
TL;DR: An upper bound on the complexity of an algorithm which finds zeros of F is established, a polynomial in terms of n, max{∥ai∥}i, and measures of the sizes of simplices in S.
Abstract: LetS be a triangulation of ℂ andf(z) = zd +ad−1zd−1+⋯+a0, a complex polynomial. LetF be the piecewise linear approximation off determined byS. For certainS, we establish an upper bound on the complexity of an algorithm which finds zeros ofF. This bound is a polynomial in terms ofn, max{∥ai∥}i, and measures of the sizes of simplices inS.
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TL;DR: In this paper, the octahedral simplicial algorithm was adapted for linear complementarity problems with upper and lower bounds, where the sign pattern of the linear function and the location of the points in comparison withz 0 completely govern the path of the algorithm.
Abstract: In this paper, we adapt the octahedral simplicial algorithm for solving systems of nonlinear equations to solve the linear complementarity problem with upper and lower bounds. The proposed algorithm generates a piecewise linear path from an arbitrarily chosen pointz 0 to a solution point. This path is followed by linear programming pivot steps in a system ofn linear equations, wheren is the size of the problem. The starting pointz 0 is left in the direction of one of the 2 n vertices of the feasible region. The ray along whichz 0 is left depends on the sign pattern of the function value atz 0. The sign pattern of the linear function and the location of the points in comparison withz 0 completely govern the path of the algorithm.
TL;DR: In this article, it was shown that for "most" of the maps that are consistent with A, the maximal absolute continuous invariant measure is not maximal, and the main result of this paper is that for most of them, it is possible to show that the maximal invariance is not always maximal.
Abstract: Let A be a certain irreducible 0-1 matrix and let T denote the family of piecewise linear Markov maps on [0, 1] which are consistent with A. The main result of this paper characterizes those maps in T whose (unique) absolutely continuous invariant measure is maximal, and proves that for "most" of the maps that are consistent with A, the absolutely continuous invariant measure is not maximal.
TL;DR: In this article, piecewise linear LRC circuits are described which allow a clear demonstration of "soft" and "hard" spring nonlinear resonant behavior, and Amplitude and phase response curves obtained with these circuits are also presented.
Abstract: Piecewise linear LRC circuits are described which allow a clear demonstration of ‘‘soft’’ and ‘‘hard’’ spring nonlinear resonant behavior. Amplitude‐ and phase‐response curves obtained with these circuits are also presented.
01 Jan 1985
TL;DR: Using Lagrangian coordinates, the energy release rate, G, is the derivative of the energy with respect to the crack length as mentioned in this paper, and G is a surface integral of the Laplace operator.
Abstract: The energy release rate, G, is the derivative of the energy with respect to the crack length. Using Lagrangian coordinates, we can derive an expression of G as a surface integral, which is mathematically equivalent to other well known expressions as the J integral of Rice or the expression in terms of stress intensity factors. Using interior error estimates, we derive an error estimate of O (h l−ɛ) on G by using piecewise linear elements. For sake of simplicity, we present these estimates for the Laplace operator. The numerical trials, which show a very good stability of the method, were performed for the elasticity system.
TL;DR: The convergence properties of the heat balance integral method are discussed in this article, where it is shown that with a particular mode of subdivision and a piecewise linear profile, the approximate solution of a simple conduction problem converges formally to the exact solution.
Abstract: The convergence properties of the heat balance integral method are discussed. It is shown that, with a particular mode of subdivision and a piecewise linear profile, the approximate solution of a simple conduction problem converges formally to the exact solution.
TL;DR: In this paper, a closed form solution to Burgers' equation on an infinite domain has been obtained for "random sawtooth" continuous initial conditions defined on a finite domain, which is used to compute statistical measures such as skewness and flatness factors, energy decay rates, and the temporal evolution of velocity autocorrelations and energy spectra.
Abstract: A closed form solution to Burgers’ equation on an infinite domain has been obtained for ‘‘random sawtooth’’ continuous initial conditions defined on a finite domain. The ‘‘turbulent’’ solution is than used to compute statistical measures such as skewness and flatness factors, energy decay rates, and the temporal evolution of velocity autocorrelations and energy spectra.
TL;DR: A new algorithm for structural pattern recognition for image understanding is presented, made according to a hypothesis-accumulation procedure followed by a peak picking search in a two dimensional array.
TL;DR: In this article, the existence of an infinite family of propagating multiple pulse solutions of a piecewise linear version of the FitzHugh-Nagumo nerve conduction equations was shown.
01 Sep 1985
TL;DR: A least squared error algorithm is presented for fitting a piecewise linear function to observed data, when the slope of the function is allowed to change only at specified points, where the locations of possible changes in trend are known.
Abstract: : A least squared error algorithm is presented for fitting a piecewise linear function to observed data, when the slope of the function is allowed to change only at specified points The algorithm can be used to estimate piecewise linear trends in data, where the locations of possible changes in trend are known Furthermore, it can be used to reduce large quantities of data to manageable sizes In addition, the algorithm is robust to problems of data dropout provided it is used cautiously An example of a possible application is the fitting of a linear segment bathythermal profile (temperature vs depth) to a large quantity of data Keywords: Canada; underwater acoustics; linear regression; numerical analysis (Author)
01 Jan 1985
TL;DR: In this paper, the authors present a method with finite termination for piecewise linear functions with the same properties as the ellipsoid method, but with a more decisive use of convexity.
Abstract: The motivations for constructing algorithms with the properties specified in the title of this paper come from two sources. The first is that the ellipsoid method (see e.g. Shor (1982) and Sonnevend (1983)) has a slow (asymptotic) convergence for functions of the above two classes. The second arises since the popular idea (practice) that the globalization of convergence for the asymptotically fast quasi-Newton methods should be achieved by the application of line search strategies (these are described in Stoer (1980); bundle methods are described in Lemarechal et al. (1981)) becomes rather questionable if function and subgradient evaluations are costly and if the function is “stiff”, i.e. has badly conditioned or strongly varying second derivatives (Hesse matrixes). Indeed, line search uses — intuitively speaking — the local information about the function only for local prediction, while in the ellipsoid method the same information is used to obtain a global prediction (based on a more decisive use of the convexity). In the bundle (e-subgradient) methods the generation of a “useable” descent direction (not speaking about the corresponding line search) may require — for a nonsmooth f (in the “zero-th” steps) — a lot of function (subgradient evaluations). The important feature of the ellipsoid method, which will be used here to obtain a method with finite termination (i.e. exact computation of f*) for piecewise linear functions (which is very important for the solution of general linear programming problems), is that it provides us with (asymptotically exact) lower bounds for the value of*.
01 Jun 1985
TL;DR: It is expected that the approach can be extended to solve large-scale problems with convex separable objective functions.
Abstract: Based on computational experiments with different approaches to convex separable network flow problems a hybrid algorithm is developed and implemented. Phase one of the algorithm uses a rapidly converging series of piecewise linear secant approximations in order to determine a good solution within some distance of the optimum. Starting from this solution, a feasible direction method, based on reduced Newton directions, is used in the second phase of the algorithm to determine the optimal solution. Since nonlinear network flow problems tend to be degenerate, special emphasis is put on the construction of a basis that yields a strictly positive step length at the beginning of phase two of the hybrid algorithm.
TL;DR: A network synthesis model to be applied to the long-range transmission planning expansion that considers simultaneously two objectives: - the minimization of equipment investments and the satis-faction of an electric performance index.
TL;DR: The special case of an input consisting of two equal-amplitude carriers is considered in detail and the results are found to be very accurate and will help in deciding whether the piecewise linear limiter will produce optimal or suboptimal results under specific traffic and criterion of optimality.
Abstract: The performance of the piecewise linear limiter with multi-carrier input signal with arbitrary carrier amplitudes is analysed by using a simple, accurate and general approach. The limiter characteristic is expanded as an infinite Fourier series and convergent series expressions are obtained for the output carriers and intermodu-lation products. The special case of an input consisting of two equal-amplitude carriers is considered in detail and the results are found to be very accurate. This result will help in deciding whether the piecewise linear limiter will produce optimal or suboptimal results under specific traffic and criterion of optimality.
TL;DR: In this paper, a piecewise-linear stress-strain law for structural members characterized by a single stress component is presented, which makes recourse to the absolute value function and does not require the auxiliary variables (plastic multipliers and yield functions) encountered in traditional descriptions of piecewise linear laws.