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31.
Günther Nürnberger 《Numerical Functional Analysis & Optimization》2013,34(4):399-421
The set of functions in C(T) which have a strongly unique best approximation from a given finite-dimensional subspace is denoted by SU(G). Since strong unicity plays an important role in numerical computations and since there the functions are only known up to some error, it is natural to ask what are the functions from the interior of SU(G). A complete characterization of those functions is given and the result is applied to weak Chebyshev and spline subspaces. 相似文献
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This paper studies problems of nonuniqueness for the metric projection ofC(T),T a compact Hausdorff space, onto a finite-dimensional subspaceG, and discusses the results for polynomial spline approximation. Among others, we prove that the metric projection ofC[a, b] ontoS
k,n
, the space of polynomial splines of degree less than or equal ton withk simple knots in (a, b), is lower semicontinuous on an open, dense subset ofC[a, b] and, consequently, any standard selection of the projection is continuous on this subset. We further show that continuous selections are not so easy to construct.Communicated by Ronald A. DeVore. 相似文献
35.
Nrnberger Gnther Schumaker Larry L. Zeilfelder Frank 《Advances in Computational Mathematics》2004,21(3-4):357-380
We describe local Lagrange interpolation methods based on C 1 cubic splines on triangulations obtained from arbitrary strictly convex quadrangulations by adding one or two diagonals. Our construction makes use of a fast algorithm for coloring quadrangulations, and the overall algorithm has linear complexity while providing optimal order approximation of smooth functions. 相似文献
36.
This paper presents results of the numerical simulation of periodically unsteady flows with focus on turbomachinery applications.
The unsteady CFD solver used for the simulations is based on the Reynolds averaged Navier–Stokes equations. The numerical
scheme applies an extended version of the Spalart–Allmaras one-equation turbulence model coupled with a transition correlation.
The first example of validation consists of boundary layer flow with separation bubble on a flat plate, both under steady
and periodically unsteady main flow conditions. The investigation includes a variation of the major parameters Strouhal number,
amplitude, and Reynolds number. The second, more complex test case consists of the flow through a cascade of turbine blades
which is influenced by wakes periodically passing over the cascade. The computations were carried out for two different blade
loadings. The results of the numerical simulations are discussed and compared with experimental data in detail. Special emphasis
is given to the investigation of boundary layers with regard to transition, separation and reattachment under the influence
of main flow unsteadiness.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
37.
Summary An algorithm for computing a set of knots which is optimal for the segment approximation problem is developed. The method yields a sequence of real numbers which converges to the minimal deviation and a corresponding sequence of knot sets. This sequence splits into at most two subsequences which converge to leveled sets of knots. Such knot sets are optimal. Numerical results concerning piecewise polynomial approximation are given. 相似文献
38.
Summary.
We describe algorithms for constructing point sets at which interpolation by
spaces of bivariate splines of arbitrary degree and smoothness is
possible. The splines are defined on rectangular partitions adding
one or two diagonals to each rectangle. The interpolation sets
are selected in such a way that the grid points of the partition
are contained in these sets, and no large linear systems have to be solved.
Our method is to generate a net of line segments and to choose point sets in
these segments which satisfy the Schoenberg-Whitney condition for
certain univariate spline spaces such that a principle of degree
reduction can be applied. In order to include the grid points in the
interpolation sets, we give a sufficient Schoenberg-Whitney type
condition for interpolation by bivariate splines supported in certain cones.
This approach is completely different
from the known interpolation methods for bivariate splines of degree at most
three. Our method is illustrated by some numerical examples.
Received
October 5, 1992 / Revised version received May 13, 1994 相似文献