In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the...Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present PD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.展开更多
In this paper,a new third type S.N.Bernstein interpolation polynomial H n(f;x,r) with zeros of the Chebyshev ploynomial of the second kind is constructed. H n(f;x,r) converge uniformly on [-1,1] for any continuous fun...In this paper,a new third type S.N.Bernstein interpolation polynomial H n(f;x,r) with zeros of the Chebyshev ploynomial of the second kind is constructed. H n(f;x,r) converge uniformly on [-1,1] for any continuous function f(x) . The convergence order is the best order if \{f(x)∈C j[-1,1],\}0jr, where r is an odd natural number.展开更多
A kind of generalization of the Curve Type Node Configuration is given in this paper, and it is called the generalized node configuration CTNCB in Rs(s > 2). The related multivariate polynomial interpolation proble...A kind of generalization of the Curve Type Node Configuration is given in this paper, and it is called the generalized node configuration CTNCB in Rs(s > 2). The related multivariate polynomial interpolation problem is discussed. It is proved that the CTNCB is an appropriate node configuration for the polynomial space Pns(s > 2). And the expressions of the multivariate Vandermonde determinants that are related to the Odd Curve Type Node Configuration in R2 are also obtained.展开更多
In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbit...In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.展开更多
文摘In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
文摘Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present PD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.
文摘In this paper,a new third type S.N.Bernstein interpolation polynomial H n(f;x,r) with zeros of the Chebyshev ploynomial of the second kind is constructed. H n(f;x,r) converge uniformly on [-1,1] for any continuous function f(x) . The convergence order is the best order if \{f(x)∈C j[-1,1],\}0jr, where r is an odd natural number.
基金the Science and Technology Project of Jiangxi Provincial Department of Education([2007]320)
文摘A kind of generalization of the Curve Type Node Configuration is given in this paper, and it is called the generalized node configuration CTNCB in Rs(s > 2). The related multivariate polynomial interpolation problem is discussed. It is proved that the CTNCB is an appropriate node configuration for the polynomial space Pns(s > 2). And the expressions of the multivariate Vandermonde determinants that are related to the Odd Curve Type Node Configuration in R2 are also obtained.
基金Foundation item： Supported by the National Natural Science Foundation of China（10626045）
文摘In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.
