In this paper, we consider the extrapolation method for second order elliptic problems on general meshes and derive a type of finite element expansion which is dependent of the triangulation. It allows to prove the effectiveness of the extrapolation on general meshes and also validates the extrapolation method can be applied on the automatically produced meshes of the general computing domains....

Given a truncated portion of a band-limited image with known x and y bandwidths, the extrapolation problem is to determine the signal over all x and y. An iterative extrapolation algorithm, recently proposed by Gerchberg, requires only the repeated operations of Fourier transformation and truncation. A coherent optical processor is presented that implements Gerchberg's iterative extrapolation a...

A static Partial Differential Equation (PDE) approach is presented for multidimensional extrapolation under the assumption that a level set function exists which separates the region of known values from the region to be extrapolated. Arbitrary orders of polynomial extrapolation can be obtained through solutions of a series of static linear PDEs. Fast sweeping methods of first and second orders...

We discuss the interpolation strategies related to Richardson extrapolation and repeated Richardson extrapolation. We emphasize that, in most computations, the interest is in obtaining accurate solution on the current computational grid, not that on the coarse level grids on which the extrapolated solutions reside. We tackle the interpolation issue that has largely been overlooked in Richardson...

Riemannian wavefield extrapolation is a technique for one-way extrapolation of acoustic waves. Riemannian wavefield extrapolation generalizes wavefield extrapolation by downward continuation by considering coordinate systems different from conventional Cartesian ones. Coordinate systems can conform with the extrapolated wavefield, with the velocity model or with the acquisition geometry. When c...

CONTEXT An estimated correlation between 2 variables is valid only within the range of observed data. Extrapolation is risky and should be performed with caution. METHODS To assess the prevalence of problems with data extrapolation in the medical literature, all articles published from January through June 2000 in BMJ, JAMA, The Lancet, and The New England Journal of Medicine (NEJM) were revi...

an alumina supported co/ni catalyst was prepared by sol-gel procedure to study the catalytic behavior during fischer-tropsch synthesis in a fixed-bed reactor. the effect of co conversion (10-50%) on hydrocarbon product distribution (ch4, c5+ and c2-c4 olefin selectivities) was studied. selectivity for ch4 decreased, while those of c5+ and olefin selectivities increased with increasing co conver...

The ability to automatically discover patterns and perform extrapolation is an essential quality of intelligent systems. Kernel methods, such as Gaussian processes, have great potential for pattern extrapolation, since the kernel flexibly and interpretably controls the generalisation properties of these methods. However, automatically extrapolating large scale multidimensional patterns is in ge...

In this paper Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition of high Eigen values of the iteration matrix to enable convergence. While extrapolation of a convergent fixed point iteration using a geometri...

Extrapolation methods are reliable, objective, inexpensive, quick, and easily automated. As a result, they are widely used, especially for inventory and production forecasts, for operational planning for up to two years ahead, and for long-term forecasts in some situations, such as population forecasting. This paper provides principles for selecting and preparing data, making seasonal adjustmen...