This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W2m spaces, The explicit constructive method f...This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W2m spaces, The explicit constructive method for the reproducing kernel in W2m space is presented, and proves the uniformity of spline interpolating operators and the best operators of interpolating approximation W2m space by reproducing kernel. The explicit expression of approximation error on a bounded ball in W2m space, and error estimation of spline operator of approximation are obtained.展开更多
In this paper, the convergency of spline interpolation operators is obtained, these spline operators are determined by linear differential operators and con straint functionals. The errors of the interpolating spline ...In this paper, the convergency of spline interpolation operators is obtained, these spline operators are determined by linear differential operators and con straint functionals. The errors of the interpolating spline with EHB fanctionals are estimated. The best approximation of linear functionals on W2m spaces are investigated, which let to a useful computational method for the approximation so- lution of higher order linear differential equations with multipoint boundary value conditions.展开更多
文摘This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W2m spaces, The explicit constructive method for the reproducing kernel in W2m space is presented, and proves the uniformity of spline interpolating operators and the best operators of interpolating approximation W2m space by reproducing kernel. The explicit expression of approximation error on a bounded ball in W2m space, and error estimation of spline operator of approximation are obtained.
文摘In this paper, the convergency of spline interpolation operators is obtained, these spline operators are determined by linear differential operators and con straint functionals. The errors of the interpolating spline with EHB fanctionals are estimated. The best approximation of linear functionals on W2m spaces are investigated, which let to a useful computational method for the approximation so- lution of higher order linear differential equations with multipoint boundary value conditions.
