In this paper, osculatory rational functions of Thiele-type introduced by Salzer (1962) are extended to the case of vector valued quantities using tile t'ormalism of Graves-Moms (1983). In the computation of the o...In this paper, osculatory rational functions of Thiele-type introduced by Salzer (1962) are extended to the case of vector valued quantities using tile t'ormalism of Graves-Moms (1983). In the computation of the osculatory continued h.actions, the three term recurrence relation is avoided and a new coefficient algorithm is introduced, which is the characteristic of recursive operation. Some examples are given to illustrate its effectiveness. A sutficient condition for cxistence is established. Some interpolating properties including uniqueness are discussed. In the end, all exact interpolating error formula is obtained.展开更多
We consider the computation of the. Cauchy principal value mtegral by quadrature formulaeof compound type, which are obtained by replacing f by a piecewise defined function F,[;]. The behaviour of the constants m the ...We consider the computation of the. Cauchy principal value mtegral by quadrature formulaeof compound type, which are obtained by replacing f by a piecewise defined function F,[;]. The behaviour of the constants m the estimates where quadrature error) is determined for fixed i and which means that not only the. order, but also the coefficient of the main term of is determined. The behaviour of these error constants is compared -with the corresponding ones obtained for the. method of subtraction of the singularity. As it turns out, these error constants have, in general, the same asymptotic behaviour.展开更多
文摘In this paper, osculatory rational functions of Thiele-type introduced by Salzer (1962) are extended to the case of vector valued quantities using tile t'ormalism of Graves-Moms (1983). In the computation of the osculatory continued h.actions, the three term recurrence relation is avoided and a new coefficient algorithm is introduced, which is the characteristic of recursive operation. Some examples are given to illustrate its effectiveness. A sutficient condition for cxistence is established. Some interpolating properties including uniqueness are discussed. In the end, all exact interpolating error formula is obtained.
文摘We consider the computation of the. Cauchy principal value mtegral by quadrature formulaeof compound type, which are obtained by replacing f by a piecewise defined function F,[;]. The behaviour of the constants m the estimates where quadrature error) is determined for fixed i and which means that not only the. order, but also the coefficient of the main term of is determined. The behaviour of these error constants is compared -with the corresponding ones obtained for the. method of subtraction of the singularity. As it turns out, these error constants have, in general, the same asymptotic behaviour.
