Showing papers on "Bilinear interpolation published in 1982"

Consistent vs. reduced integration penalty methods for incompressible media using several old and new elements

Abstract: SUMMARY The frequently used reduced integration method for solving incompressible flow problems 'a la penalty' is critically examined vis-a-vis the consistent penalty method. For the limited number of quadrilateral and hexahedral elements studied, it is shown that the former method is only equivalent to the latter in certain special cases. In the general case, the consistent penalty method is shown to be more accurate. Finally, we demonstrate significant advantages of a new element, employing biquadratic (2-D) or triquadratic (3-D) velocity and linear pressure over that using the same velocity but employing bilinear (2-D) or trilinear (3-D) pressure approximation.

Piecewise rational quadratic interpolation to monotonic data

Abstract: An explicit representation of a piecewise rational quadratic function is developed which produces a monotonic interpolant to given monotonic data. The explicit representation means that the piecewise monotonic interpolant is easily constructed and numerical experiments indicate that the method produces visually pleasing curves. Furthermore, the use of the method is justified by an 0(h) convergence result .

On stationary linear time-varying systems

Abstract: A comprehensive review of representations of linear timevarying systems is given, both in the time and in frequency domains. Subsequently a definition is given of a stationary deterministic signal. Based on this definition the notion of stationary systems is introduced. These systems have the useful property that the spectral relation between input and output has a simpler form than the corresponding relation for arbitrary time-varying systems. It is shown that causality puts rather severe constraints on the frequency mappings that can be realized by stationary linear systems. An extension of the theory of linear time-varying systems to the case of discrete-time and hybrid systems (analog input, digital output, or vice versa) is discussed. Examples of stationary systems are given, such as a decimator, a periodic sampler, and a bilinear A/D converter. Also, a recently proposed generalized sampling method is analyzed by means of the concepts discussed in this paper.

Analytical model for concrete anchorages of reinforcing bars under generalized excitations

Abstract: This report presents an analytical model for predicting the behavior of single deformed reinforcing bars embedded in confirmed concrete and subjected to generalized excitations in the range of low cycle fatigue. The model is based on a general local bond stress-slip relationship, derived from the results of an extensive study performed at Berkeley, and on either a bilinear or a simple but sufficiently accurate nonlinear stress-strain relationship for the reinforcing steel bar. An efficient numerical scheme for the integration of the governing differential equation of bond along the embedment length of the bar is presented.

Bilinearization of soliton equations

Abstract: Transformations of soliton equations into the bilinear forms involving four dependent variables are discussed. It is found that both nonlinear Schrodinger equation and classical Heisenberg ferromagnet equation are transformed into the same bilinear from, while the equation \begin{aligned} \phi_{xt}{=}\phi(1-|\phi_{t}|^{2})^{1/2} \end{aligned} shares the same bilinear form with the Pohlmeyer-Lund-Regge-Getmanov equation. Transformations of the complex sine-Gordon equation and the Landau-Lifshitz equation into the bilinear forms are also described.

A note on the existence of strictly stationary solutions to bilinear equations

Abstract: . Necessary and sufficient conditions for the existence of strictly stationary solutions to a class of bilinear equations are derived, extending the results obtained by Tong (1981) and Quinn (1982).

Industrial articulated robot linear interpolation control device

Abstract: In a control device for an industrial articulated robot, in the linear interpolation between two specified points, the distance between the two points is divided into segments, and the interpolation increments of the articulation drive axes for each interpolation internal, which correspond to the segments, are calculated for interpolation so that the interpolation increments are distributed uniformly with time.

On the Completeness of Multi-Variate Optimum Interpolation for Large-Scale Meteorological Analysis

Abstract: The Baer-Tribbia nonlinear modal initialization method implies that large-scale meteorological analyses should focus on analysis of slow mode fields. An idealized multi-variate optimum interpolation analysis is shown to produce grid point results that contain only slow modes. Variational analysis with a slow mode constraint is therefore unnecessary.

Two-dimensional digital linear interpolation system

Abstract: A two-dimensional interpolation of image data is pro­ vided for a video display system, in which a one-dimensional interpolator performs the interpolation in both dimensions with data flow control so that images can be transmitted, scaled and displayed in real time.

Analysis of linear interpolation schemes for bi-level image applications

Abstract: In the office, it is often necessary to scan a picture at a certain resolution and then reproduce it at a different (usually higher) resolution This conversion can be achieved by interpolating the

Some ‘special’ interpolation formulae for triangular and quadrilateral elements

Abstract: Presented herein are methods to generate special interpolation formulae of the following type: (i) C0 continuous interpolation over triangular elements which induces a given type of singularity for the first derivatives at one of the vertices, and yet preserves ‘rigid and constant strain’ motions, (ii) C1 continuous interpolation over triangular elements which induces a given type of singularity for second derivatives at one of the vertices.

Bilinear, dynamic single-ports and bond graphs of economic systems

Abstract: It is shown that reinvestment and inventory effects can be described in 0431 0368 bond-graph terms. The associated differential equations in price and order-flow 0431 0368 V variables are bilinear forms. These effects are the fundamental inertia and compliance 0431 0368 V 3 of economic bond graph theory. Properties of the components and example market 0431 0368 V 3 graphs are discussed.

Finite-dimensional observation-spaces for non-linear systems

Abstract: A non-linear system has the same input-output behaviour as a regular (or bilinear) system if, and only if, a certain function-space, called the observation-space, is finite-dimensional.

A new derivation of the Kustaanheimo-Stiefel variables

Abstract: First introducing the parabolic coordinates inR3, we can derive the Kustaanheimo-Stiefel (KS) variables quite simply and naturally Through this derivation it becomes clearer where and how the additional dimension is introduced and what the bilinear relation means

Interpolation of completely monotone functions

Abstract: Intervals in which Lagrange interpolation polynomials converge pointwise to the interpolated function are specified for a family of functions comprising all completely monotone functions.

A new algorithm for optimal interpolation of discrete-time stationary processes

Abstract: A new approach to the interpolation problem for multivariate stationary Gaussian processes is presented. This approach hinges on the recently developed stochastic realization theory. New representations for the optimal interpolator and interpolation error variance are derived. In particular we show that the interpolation estimate is characterized by two steady Kalman filters, one evolving forward and one backward in time. The derivation is simple and enlightening. The results appear to be of computational interest.

Multidimensional bilinear transformations

Abstract: The bilinear transformation is extended to transform multi-variable polynomials, using discrete convolution and the Kronecker product. This approach is very simple, easy for computer implementation, and useful in complex curve fitting and stability studies of discrete systems and the design of digital filters etc.

Identification of bilinear systems using relay feedback

Abstract: After expressing the response of a bilinear dynamical system in terms of a Volterra series, the filtering properties of the system are characterized in the frequency domain. The zero harmonic component of the output of a closed-loop system comprised of the bilinear system and a static relay non-linear element is approximated using basic second-order Volterra kernels. This allows estimation of bilinear system parameters based upon measurements of the average value of the closed-loop system output.