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Sparse matrix algorithms applied to dem generation
Abstract A method for generating a digital elevation model (DEM) was suggested byEbner. The heights of grid points are interpolated from arbitrarily distributed reference points using the finite element method. The requested grid heights of the DEM are defined as unknowns and estimated from the available reference points and a general curvature minimization of the interpolation surface with filtering at the reference points. This problem can be interpreted as an adjustment of indirect observations and can be solved using the least squares method. This leads to a banded structured system of normal equations in case of numbering the unknowns in a row-wise order. This ordering may not be the best strategy for the solution of the normal equations, because the band contains many zero elements. Therefore algorithms which exploit the nonzero/zero structure to better advantage have been applied in combination with the pivot strategies of “Nested Dissection” and “Minimum Degree Ordering” (OPTORD). The operational characteristics of these algorithms are compared with those of the band-algorithm for several DEM problems that vary in size to over 4000 unknowns. The result shows that the number of nonzeros and the number of essential operations can be reduced drastically when using sparse algorithms, but that because of the very high bookkeeping expenses, band algorithms are to be preferred.
Sparse matrix algorithms applied to dem generation
Abstract A method for generating a digital elevation model (DEM) was suggested byEbner. The heights of grid points are interpolated from arbitrarily distributed reference points using the finite element method. The requested grid heights of the DEM are defined as unknowns and estimated from the available reference points and a general curvature minimization of the interpolation surface with filtering at the reference points. This problem can be interpreted as an adjustment of indirect observations and can be solved using the least squares method. This leads to a banded structured system of normal equations in case of numbering the unknowns in a row-wise order. This ordering may not be the best strategy for the solution of the normal equations, because the band contains many zero elements. Therefore algorithms which exploit the nonzero/zero structure to better advantage have been applied in combination with the pivot strategies of “Nested Dissection” and “Minimum Degree Ordering” (OPTORD). The operational characteristics of these algorithms are compared with those of the band-algorithm for several DEM problems that vary in size to over 4000 unknowns. The result shows that the number of nonzeros and the number of essential operations can be reduced drastically when using sparse algorithms, but that because of the very high bookkeeping expenses, band algorithms are to be preferred.
Sparse matrix algorithms applied to dem generation
Stark, Wilhelm (Autor:in) / Steidler, Franz (Autor:in)
Bulletin géodésique ; 57
1983
Aufsatz (Zeitschrift)
Englisch
Geodäsie , Geometrie , Geodynamik , Zeitschrift , Mathematik , Mineralogie
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