Bivariate spline interpolation at grid points

1995 ◽  
Vol 71 (1) ◽  
pp. 91-119 ◽  
Author(s):  
G. Nürnberger ◽  
Th. Riessinger
Keyword(s):  
Spline Interpolation ◽  
Bivariate Spline ◽  
Grid Points ◽  
Bivariate Spline Interpolation

scholarly journals Developments in bivariate spline interpolation

2000 ◽  
Vol 121 (1-2) ◽  
pp. 125-152 ◽  
Author(s):  
G. Nürnberger ◽  
F. Zeilfelder
Keyword(s):  
Spline Interpolation ◽  
Bivariate Spline ◽  
Bivariate Spline Interpolation

scholarly journals Bivariate spline interpolation with optimal approximation order

2001 ◽  
Vol 17 (2) ◽  
pp. 181-208 ◽  
Author(s):  
O. Davydov ◽  
G. Nürnberger ◽  
F. Zeilfelder
Keyword(s):  
Spline Interpolation ◽  
Approximation Order ◽  
Optimal Approximation ◽  
Bivariate Spline ◽  
Bivariate Spline Interpolation

scholarly journals Antarctic Ice Elevation Maps From Balloon Altimetry

1982 ◽  
Vol 3 ◽  
pp. 184-188 ◽  
Author(s):  
Nadav Levanon
Keyword(s):  
Spline Interpolation ◽  
Reference Level ◽  
Constant Density ◽  
Pressure Surface ◽  
Contour Lines ◽  
Elevation Data ◽  
Special Value ◽  
Grid Points ◽  
Mapping Techniques ◽  
Spline Interpolation Technique

Antarctic ice-elevation maps are presented, based on 4 000 measurement points, analysed from traverses made by constant-density balloons. These balloons were launched during the Tropical Wind, Energy Conversion and Reference Level Experiment (TWERLE). The TWERLE data yielded daily maps of the elevation of the 150 mbar pressure surface in the southern hemisphere. These maps serve as a reference level from which the altimeter readings are subtracted to yield the ice elevation. The accuracy of the ice-elevation data is estimated at better than 60 m. The accuracy of the contouring depends on the density of measurements in the particular area. Two contouring techniques were used. One is based on generating elevation data at fixed grid-points from arbitrarily distributed measurements, using Cressman's method. The second is a surface spline interpolation technique by Duchon. The elevation data are of special value on the inland plateau areas. There, the typical distance between balloon measurements is sufficiently small, relative to the typical distance between contour lines at 100 m intervals. Furthermore, the inland areas are the least accessible to other mapping techniques.

scholarly journals Antarctic Ice Elevation Maps From Balloon Altimetry

1982 ◽  
Vol 3 ◽  
pp. 184-188 ◽  
Author(s):  
Nadav Levanon
Keyword(s):  
Spline Interpolation ◽  
Reference Level ◽  
Constant Density ◽  
Pressure Surface ◽  
Contour Lines ◽  
Elevation Data ◽  
Special Value ◽  
Grid Points ◽  
Mapping Techniques ◽  
Spline Interpolation Technique

Antarctic ice-elevation maps are presented, based on 4 000 measurement points, analysed from traverses made by constant-density balloons. These balloons were launched during the Tropical Wind, Energy Conversion and Reference Level Experiment (TWERLE). The TWERLE data yielded daily maps of the elevation of the 150 mbar pressure surface in the southern hemisphere. These maps serve as a reference level from which the altimeter readings are subtracted to yield the ice elevation.The accuracy of the ice-elevation data is estimated at better than 60 m. The accuracy of the contouring depends on the density of measurements in the particular area. Two contouring techniques were used. One is based on generating elevation data at fixed grid-points from arbitrarily distributed measurements, using Cressman's method. The second is a surface spline interpolation technique by Duchon.The elevation data are of special value on the inland plateau areas. There, the typical distance between balloon measurements is sufficiently small, relative to the typical distance between contour lines at 100 m intervals. Furthermore, the inland areas are the least accessible to other mapping techniques.

scholarly journals Value Function Iteration as a Solution Method for the Ramsey Model

2011 ◽  
Vol 231 (4) ◽  
Author(s):  
Burkhard Heer ◽  
Alfred Maußner
Keyword(s):  
Solution Method ◽  
Value Function ◽  
Spline Interpolation ◽  
Agent Model ◽  
Value Function Iteration ◽  
Speed Up ◽  
Grid Points ◽  
High Level ◽  
The Value Function ◽  
Speed And Accuracy

SummaryValue function iteration is one of the standard tools for the solution of dynamic general equilibrium models if the dimension of the state space is one ore two. We consider three kinds of models: the deterministic and the stochastic growth model and a simple heterogenous agent model. Each model is solved with six different algorithms: (1) simple value function iteration as compared to (2) smart value function iteration neglects the special structure of the problem. (3) Full and (4) modified policy iteration are methods to speed up convergence. (5) linear and (6) cubic interpolation between the grid points are methods that enhance precision and reduce the size of the grid. We evaluate the algorithms with respect to speed and accuracy. Accuracy is defined as the maximum absolute value of the residual of the Euler equation that determines the household’s savings. We demonstrate that the run time of all algorithms can be reduced substantially if the value function is initialized stepwise, starting on a coarse grid and increasing the number of grid points successively until the desired size is reached.We find that value function iteration with cubic spline interpolation between grid points dominates the other methods if a high level of accuracy is needed.

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

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