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Showing papers on "Piecewise published in 1985"


Journal ArticleDOI
TL;DR: In this article, it was shown that a three times continuously differentiable conductivity is identifiable by boundary measurements, and that a similar result holds for piecewise real-analytic conductivities.
Abstract: : In a recent paper the authors showed that an unknown real-analytic conductivity gamma may be determined from static boundary measurements. In this document they extend this analysis by demonstrating that a similar result holds for piecewise real-analytic conductivities. In addition, for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements. Originator-supplied keywords include: Inversion, Convergence, Algorithms, Estimates, Coefficients.

428 citations


Journal ArticleDOI
TL;DR: The quasi-compactness of the Perron-Frobenius operator of piecewise monotonic transformations with Holder-continuous inverse was shown in this article, where the inverse of the derivative is bounded p-variation.
Abstract: We prove the quasi-compactness of the Perron-Frobenius operator of piecewise monotonic transformations when the inverse of the derivative is Holder-continuous or, more generally, of bounded p-variation.

170 citations


Journal ArticleDOI
TL;DR: A technique is presented that makes it possible to piece together two algebraic surface patches with any degree of cross-boundary derivative continuity.

155 citations


Journal ArticleDOI
TL;DR: In this article, an optimization method was developed to identify parameter structure as well as its values in connection with the inverse problem in groundwater modeling, where the complexity of the parameter structure is determined by the quantity and quality of observation data.
Abstract: This paper develops an optimization method that can be used to identify parameter structure as well as its values in connection with the inverse problem in groundwater modeling. The complexity of the parameter structure is determined by the quantity and quality of observation data. Output least square error is used as the criterion of identification. Sensitivity coefficients at finite element nodes are evaluated by the variational method. The problem of identifying the parameter structure is formulated as a problem of combinatorial optimization. A new parameterization technique is presented for describing the parameter structure. It can represent various distributions of parameters from piecewise constant to continuous variability. Based on this representation, the combinatorial optimization problem for determining the parameter structure is then solved by a simple one-at-a-time searching procedure. Numerical experimentations are used to demonstrate the efficiency and practicality of the proposed method.

137 citations


Journal ArticleDOI
D. Verms1
TL;DR: In this article, the trajectories of piecewise deterministic Markov processes are solved by an ordinary (vector)differential equation with possible random jumps between the different integral curves, and both continuous deterministic motion and the random jumps of the processes are controlled in order to minimize the expected value of a performance functional consisting of continuous, jump and terminal costs.
Abstract: The trajectories of piecewise deterministic Markov processes are solutions of an ordinary (vector)differential equation with possible random jumps between the different integral curves. Both continuous deterministic motion and the random jumps of the processes are controlled in order to minimize the expected value of a performance functional consisting of continuous, jump and terminal costs. A limiting form of the Hamilton-Jacobi-Bellman partial differential equation is shown to be a necessary and sufficient optimality condition. The existence of an optimal strategy is proved and acharacterization of the value function as supremum of smooth subsolutions is also given. The approach consists of imbedding the original control problem tightly in a convex mathematical programming problem on the space of measures and then solving the latter by dualit

118 citations


Journal ArticleDOI
TL;DR: In this article, the problem of determining an appropriate grading of a mesh for piecewise polynomial interpolation and for approximate solution of two-point boundary-value problems by finite difference or finite element methods is considered.
Abstract: We consider the problem of determining an appropriate grading of a mesh for piecewise polynomial interpolation and for approximate solution of two-point boundary-value problems by finite difference or finite element methods. An analysis of optimality of the mesh and optimal grading functions in various norms and seminorms for the interpolation problem leads to the formulation of an adaptive mesh redistribution algorithm for boundary-value problems in one dimension. Error estimates are given and numerical results presented to demonstrate the performance of the scheme and compare alternative redistribution criteria.

110 citations


Journal ArticleDOI
TL;DR: The concept of coefficient shift matrix is introduced to represent delay variables in block pulse series and the optimal control of a linear delay system with quadratic performance index is studied via block pulse functions.
Abstract: The concept of coefficient shift matrix is introduced to represent delay variables in block pulse series. The optimal control of a linear delay system with quadratic performance index is then studied via block pulse functions, which convert the problems into the minimization of a quadratic form with linear algebraic equation constraints. The solution of the two-point boundary-value problem with both delay and advanced arguments is circumvented. The control variable obtained is piecewise constant.

71 citations


Book ChapterDOI
TL;DR: In this paper, a class of piecewise C 2 Lozi-like maps is considered and the existence of invariant measures with absolutely continuous conditional mea-sures on unstable manifolds is proved.
Abstract: We consider a class of piecewise C 2 Lozi-like maps and prove the existence of invariant measures with absolutely continuous conditional mea­sures on unstable manifolds

67 citations


Journal ArticleDOI
TL;DR: Two special classes of regular events are studied: the piecewise testable events and the events of dot-depth one, especially in terms of their minimal automaton.

64 citations


Journal ArticleDOI
TL;DR: The v-splines are generalized to geometric spline curves and the computational equations of quintic splines curves with curvature and torsion continuity are given.

58 citations


Journal ArticleDOI
TL;DR: In this paper, sufficient conditions for the existence of a bounded interpolating projection onto subspaces of C[0, 1] are found, and for spaces of piecewise polynomial functions the projection can be bounded by the B-spline basis condition number.

Journal ArticleDOI
TL;DR: In this paper, the optimal stopping time problem for piecewise deterministic processes with deterministic dynamics between random jumps is studied, and W4,00-existence results and probabilistic representations for the solutions of the problem in bounded domains and in R are given.
Abstract: This paper concerns the optimal stopping time problem for a piecewise deterministic process. The process has deterministic dynamics between random jumps. The as¬sociated dynamic programming equation is a variational inequality with integral and (first order) differential terms. Our main results are W4,00-existence results and probabilistic representations for the solutions of the optimal stopping time problem in bounded domains and in R. We also generalize these results to the case when the state space is “countable folds” of Euclidean space

Journal ArticleDOI
TL;DR: The problem of finding convex spline interpolants with minimal mean curvature leads to a quadratic optimization problem of special structure and a corresponding dual problem without constraints is derived.
Abstract: The problem of finding convex spline interpolants with minimal mean curvature leads to a quadratic optimization problem of special structure. In the present note a corresponding dual problem without constraints is derived. Its objective function is piecewise quadratic and therefore admits an effective numerical treatment.

Patent
16 Aug 1985
TL;DR: In this paper, the authors propose a matching process for signal matching, in which the two signals are matched with disparities there between resolved and removed responsive to the best match values, and a neighborhood of potentially interacting matches are evaluated.
Abstract: A process for signal matching. The process is general and can be applied to matching signals of arbitrary dimension. To implement the process, a suitable discretized description of the two signals to be matched is defined. Such descriptions can be the local signal extrema or any other qualitative signal significant points of interest or features. Allowable feature matches and values for matches are defined, and determined for all potential matches. Matches are confined to the features within defined matching windows and are mapped for each significant point. Within a defined similarity disparity window, a neighborhood of potentially interacting matches are evaluated. Matches within a neighborhood contribute to the decision about the appropriate match for each significant point to determine a composite similarity weighted best value match for each point. Mapping is piecewise continuous. The two signals are matched with disparities therebetween resolved and removed responsive to the best match values. Following the coherence process, the overall process of the present invention provides a superposition of several such piecewise transformations. In an illustrated application domain, a stereo correspondence technique provides for matching of figurally similar three dimensional images, according to a simple no iterative, parallel and local process that can successfully detect disparities of opaque as well as transparent surfaces.

Journal ArticleDOI
TL;DR: It is shown that the Fritsch and Carlson algorithm yields a third-order approximation, while a modification is fourth-order accurate.
Abstract: Fritsch and Carlson [SIAM J. Numer. Anal., 17 (1980), pp. 238–246] developed an algorithm which produces a monotone $C^1 $ piecewise cubic interpolant to a monotone function. We show that their algorithm yields a third-order approximation, while a modification is fourth-order accurate.

Journal ArticleDOI
TL;DR: This paper considers a finite element method for the Stokes problem on a rectangular domain based on piecewise bilinear velocities and piecewise constant pressures on a uniform rectangular grid and proposes an iterative variant of the method based on multigrid techniques which seems to yield a simpler algorithm.
Abstract: We consider a finite element method for the Stokes problem on a rectangular domain based on piecewise bilinear velocities and piecewise constant pressures on a uniform rectangular grid. It is shown that by a simple stabilization strategy the method can be implemented in a convergent multigrid procedure. Introduction. One of the most natural ways of discretizing the Stokes equations on a two-dimensional rectangular domain is to apply the finite element techniques with continuous piecewise bilinear velocities and piecewise constant pressures on a rectangular grid. This method is easily extended to more general quadrilateral meshes and it has proved to be quite effective in practice. The convergence analysis of the method was first carried out in (10) on a rectangular domain. In (12) the estimates of (10) are improved and extended to more general quadrilateral meshes. So far, the above method has been used mainly in connection with direct band solvers, usually combined with penalty/perturbation techniques to eliminate the pressure (9). In this paper we consider an iterative variant of the method based on multigrid techniques. Such an algorithm seems attractive, especially since the un- derlying finite-difference equations are relatively simple. Multigrid methods for the Stokes problem and for more general elliptic systems were considered previously by Hackbusch (8) and Verfurth (14). In (14) it is shown that a convergent multigrid algorithm for the Stokes problem can be constructed by appropriately scaling the variables, provided that the underlying finite element scheme satisfies the Babu?ka-Brezzi stability condition (2), (5). In our case, however, the finite element method is not stable in this sense, and we have not been able to show that the straightforward application of the algorithm proposed in (14) yields a convergent process. Therefore, we suggest first modifying the finite element method in such a way that it becomes stable in the ordinary sense. The usual way of stabilizing an unstable mixed method is to add more velocity (or primary) variables. A classical example of this is the quadratic/linear velocity-pres- sure element of Crouzeix and Raviart (6), where added "bubble" functions act as stabilizers in the velocity space. Increasing the dimension of the velocity space would be an alternative in our case. However, we propose another method which seems to yield a simpler algorithm. It is based on adding an extra stabilizing term into the

Journal ArticleDOI
TL;DR: In this paper, a method of constructing periodic solutions in non-linear dynamic systems with a finite number of degrees of freedom, which enables a solution to be found in the form of a series, from periodic piecewise smooth functions of a fairly simple form is proposed.

Journal ArticleDOI
01 Apr 1985
TL;DR: For translation invariant spaces S, a necessary and sufficient condition for the eventual denseness of the corresponding scaled spaces S sub h is that S contain a stable and locally supported partition of unity as discussed by the authors.
Abstract: : This document shows that for certain translation invariant spaces S, a necessary and sufficient condition for the eventual denseness of the corresponding scaled spaces S sub h is that S contain a stable and locally supported partition of unity. These results have been motivated by recent work on approximation by multivariate piecewise polynomials on regular meshes. (Author)

Book ChapterDOI
01 Jun 1985
TL;DR: A new interpolation technique is introduced that when applied to piecewise smooth data gives high-order accuracy wherever the function is smooth but avoids having a Gibbs-phenomenon at discontinuities.
Abstract: In this paper we describe high-order accurate Godunov-type schemes for the computation of weak solutions of hyperbolic conservation laws that are essentially non-oscillatory We show that the problem of designing such schemes reduces to a problem in approximation of functions, namely that of reconstructing a piecewise smooth function from its given cell averages to high order accuracy and without introducing large spurious oscillatons To solve this reconstruction problem we introduce a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy wherever the function is smooth but avoids having a Gibbs-phenomenon at discontinuities

Journal ArticleDOI
TL;DR: In this paper, a non-planar version of the PCKFM was developed and applied to the AGARD wing-tail configuration and the interference aerodynamic forces were compared with results obtained using other numerical methods.
Abstract: The rapid convergence characteristics and high accuracy of the three-dimensional piecewise continuous kernel function method are tested on a nonplanar configuration. The nature of the singularity of the three-dimensional kernel function for the nonplanar configuration is examined and anomalies associated with almost adjoining lifting surfaces are explained. Applications are made using the standard AGARD wing-tail configuration and the interference aerodynamic forces are compared with results obtained using other numerical methods. 7 to compute aerodynamic forces on a nonplanar configuration is de- scribed. The nature of the singularity of the nonplanar kernel function is examined and its characteristics are taken into con- sideration while developing the nonplanar version of the PCKFM. The numerical results obtained using the PCKFM for the above-mentioned AGARD examples are compared with results obtained using other methods. analysis as such. All other pressure singularities are ignored during the analysis, and their consideration is limited to the determination of the boundaries between the different boxes. The problems associated with the basic three-dimensional PCKFM were treated in Refs. 5-7. Additional problems which arise from the three-dimensional nonplanar flow configura- tions and which require the formulation of numerical tech- niques for the successful application of the method are ad- dressed in this paper. An example of a wing with geometrical discontinuities divided into boxes is given in Fig. 1. The pressure distribution in each of the boxes formed by the PCKFM can, therefore, be represented in general terms by the following expression:


Journal ArticleDOI
TL;DR: In the present paper, a smoothing algorithm for bicubic spline surfaces is presented, having the piecewise cubic boundaries of the patches fixed, the algorithm chooses adequate twists factors in order to increase the smoothness.

Journal ArticleDOI
TL;DR: The crucial problem of estimating changing variance of the model was solved by the techniques of piecewise modeling and local modeling and the extraction of micro earthquake signal was shown to exemplify the proposed procedures.

Journal ArticleDOI
TL;DR: In this article, the stability of the solution of systems of ordinary differential equations with impulse effect under persistent disturbances is investigated for the first time and definitions for stability and unstability of the system considered are introduced.


Journal ArticleDOI
TL;DR: In this paper, an approach to multivariate interpolation is described, which is applicable in arbitrary dimensions and can generate surfaces of arbitrary smoothness, and is accomplished by tesselating the polyhedral domain into simplices and using one-dimensional algorithms to construct interpolants first on edges and then successively on higher order faces by blending methods.
Abstract: An approach to multivariate interpolation is described. The algorithm is applicable in arbitrary dimensions, and can generate surfaces of arbitrary smoothness. This is accomplished by tesselating the (polyhedral) domain into simplices and using one-dimensional algorithms to construct interpolants first on edges and then successively on higher order faces by blending methods. The result is a piecewise rational function of a high degree which has the prescribed global smoothness and interpolates to the original data. The interpolants are local, i.e. their evaluation at a point requires only data on the simplex that the point resides in. The schemes require data of the same degree as the degree of global smoothness. The degree of polynomial precision is greater than or equal to the degree of smoothness. The approach derives its power and simplicity from the fact that derivatives in directions perpendicularly across faces are incorporated directly as data.

Journal ArticleDOI
TL;DR: In this article, the ground state of a one-dimensional model with two sublattices is calculated, which is a variation of the piecewise parabola Frenkel-Kontorova model, and the phase diagram of this model as a function of the chemical potential and the electric field is explicitly calculated.
Abstract: The ground state of a one-dimensional model with two sublattices which is a variation of the piecewise parabola Frenkel-Kontorova model. is explicitly calculated. This model involves an additional parameter (the electric field) which breaks a (non-symmorphic) symmetry element when it is non-zero. At a fixed commensurability ratio :. it is shown that the polarisation curve as a function of the electric field is the sum of a linear part and a staircase, This staircase is either a harmless staircase (: rational) with true first-order transitions or a Devil's staircase ( :irrational). The plateaus of these staircases are obtained when an unusual condition (called subcommensurability condition) which involves the relative phase shift between the two sublattices is fulfilled. The phase diagram of this model as a function of the chemical potential and the electric field is explicitly calculated. It is entirely filled by the domain of stability of phases which are characterised both by a rational commensurability ratio and a polarisation fulfilling the subcommensurability condition. These domains are polygons with an infinite number of edges. At fixed electric field. the commensurability ratio {varies as a function of the chemical potential as a Devil's staircase with plateaus at rational values of :but these ones have widths submitted to selection rules related to the model symmetry. The corresponding curve for the variation of the polarisation is a new 'devilish' function called a Manhattan profile. This curve exhibits infinitely many plateaus but unlike a Devil's staircase is alternatively increasing and decreasing infinitely many times by discontinuities. The results obtained on this model are favorably compared with experimental results in thiourea. Predictions are also given and in particular a scintil- lating variation of the polarisation when the temperature or the pressure varies (which is the consequence of the Manhattan profile). Finally. it is noted that the method used for the exact solution of this model can be extended to a wider class of other models: (1) with several sublattices. (2) with long-range interactions. (3) with lattices at any dimension. which should in the future allow more complex models, which approach more closely the real systems. to be solved exactly.

Journal ArticleDOI
TL;DR: In this paper, the problem of the condition of matrices arising in the numerical solution of integral equations of the first kind by Galerkin and collocation schemes was investigated and a lower bound on the matrix condition number was found and its behavior as a function of the smoothness of the kernel of the original equation was studied.

Journal ArticleDOI
TL;DR: A new algorithm for piecewise bicubic interpolation to bivariate data on a rectangular mesh is described and the Hermite form is used to represent the resulting surface.

Journal ArticleDOI
01 Oct 1985-Calcolo
TL;DR: In this paper, a one-step method for delay differential equations, which is equivalent to an implicit Runge-Kutta method, was proposed, which approximates the solution in the whole interval with a piecewise polynomial of fixed degree n.
Abstract: We study a one-step method for delay differential equations, which is equivalent to an implicit Runge-Kutta method. It approximates the solution in the whole interval with a piecewise polynomial of fixed degree n. For an appropiate choice of the mesh points, it provides uniform convergence 0(hn+1) and the superconvergence 0(h2n) at the nodes.