General interpolation formulae for barycentric interpolation and barycen- tric rational Hermite interpolation are established by introducing multiple parameters, which include many kinds of barycentric interpolation a...General interpolation formulae for barycentric interpolation and barycen- tric rational Hermite interpolation are established by introducing multiple parameters, which include many kinds of barycentric interpolation and barycentric rational Her- mite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method.展开更多
In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate ...In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate of the preceding interpolation formula.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
We calculate the electrical and thermal conductivity of hydrogen for a wide range of densities and temperatures by using molecular dynamics simulations informed by density functional theory.On the basis of the corresp...We calculate the electrical and thermal conductivity of hydrogen for a wide range of densities and temperatures by using molecular dynamics simulations informed by density functional theory.On the basis of the corresponding extended ab initio data set,we construct interpolation formulas covering the range from low-density,high-temperature to high-density,low-temperature plasmas.Our conductivity model repro-duces the well-known limits of the Spitzer and Ziman theory.We compare with available experimental data andfind very good agreement.The new conductivity model can be applied,for example,in dynamo simulations for magneticfield generation in gas giant planets,brown dwarfs,and stellar envelopes.展开更多
In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2...In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2]. namely an interpolation formula of the difference of higher order. Finally we give their applications.展开更多
We investigate the process of lepton-number-violating pion decay,which dominates the nuclear neutrinoless double beta decay induced by the short-range operator within the type-Ⅰ seesaw mechanism.The type-Ⅰ seesaw me...We investigate the process of lepton-number-violating pion decay,which dominates the nuclear neutrinoless double beta decay induced by the short-range operator within the type-Ⅰ seesaw mechanism.The type-Ⅰ seesaw mechanism leads to the Dirac and Majorana mass terms of neutrinos by introducing the gauge-singlet righthanded neutrinos,which are often called sterile neutrinos.Applying the chiral perturbation theory,we calculate the transition amplitudes for light and heavy sterile neutrinos up to O(Q^(2)/Λ_(χ)^(2)),where Q is the typical low-energy scale in this process and Λ_(χ) the chiral symmetry breaking scale.We then adopt a naive interpolation formula of mass dependence to obtain the amplitude in the full mass range and briefly discuss its validity.展开更多
At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational inter...At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.展开更多
By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of inter...By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of interpolation formulae are obtained by adopting different approximate methods, to try to enhance the accuracy of the interpolatory operator. A theoretical study proves the two-level convergence of these Gauss-Seidel-type MG methods. A series of numerical experiments is presented to evaluate the relative performance of the methods with respect to the convergence factor, CPU-time(for one V-cycle and the setup phase) and computational complexity.展开更多
Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators.We begin by describing Chebfun's fa...Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators.We begin by describing Chebfun's fast capabilities for Clenshaw-Curtis and also Gauss-Legendre,-Jacobi,-Hermite,and-Laguerre quadrature,based on algorithms of Waldvogel and Glaser,Liu and Rokhlin.Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles,fractional derivatives and integrals,functions defined on unbounded intervals,and the fast computation of weights for barycentric interpolation.展开更多
In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a s...In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.展开更多
This paper presents new methods for spacecraft relative pose estimation using the Unscented Kalman Filter(UKF),taking into account non-additive process and measurement noises.A twistor model is employed to represent t...This paper presents new methods for spacecraft relative pose estimation using the Unscented Kalman Filter(UKF),taking into account non-additive process and measurement noises.A twistor model is employed to represent the spacecraft's relative 6-DOF motion of the chaser with respect to the target,expressed in the chaser body frame.The twistor model utilizes Modified Rodrigues Parameters(MRPs)to represent attitude with a minimal number of parameters,eliminating the need for the normalization constraint that exists in the quaternion-based model.Additionally,it incorporates both relative position and attitude in a single model,addressing kinematic coupling of states and simplifying the estimator design.Despite numerous existing pose estimation algorithms,many rely on the simplification of additive noise assumptions.This work enhances the robustness and improves the convergence of non-additive noise algorithms by deriving two methods to accurately approximate process and measurement noise covariance matrices for systems with non-additive noises.The first method utilizes the Stirling Interpolation Formula(SIF)to obtain equivalent process and measurement noise covariance matrices.The second method employs State Noise Compensation(SNC)to derive the equivalent process noise covariance matrix and uses SIF to compute the equivalent measurement noise covariance matrix.These methods are integrated into the UKF framework for estimating the relative pose of spacecraft in proximity operations,demonstrated through two scenarios:one with a cooperative target using Position Sensing Diodes(PSDs)and another with an uncooperative target using LiDAR for 3-D imaging.The effectiveness of these methods is validated against others in the literature through Monte Carlo simulations,showcasing their faster convergence and robust performance.展开更多
基金supported by the grant of Key Scientific Research Foundation of Education Department of Anhui Province, No. KJ2014A210
文摘General interpolation formulae for barycentric interpolation and barycen- tric rational Hermite interpolation are established by introducing multiple parameters, which include many kinds of barycentric interpolation and barycentric rational Her- mite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method.
文摘In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate of the preceding interpolation formula.
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.
基金supported by the Priority Program SPP 1992 of the German Science Foundation(DFG)The Diversity of Exoplanets under project number 362460292.
文摘We calculate the electrical and thermal conductivity of hydrogen for a wide range of densities and temperatures by using molecular dynamics simulations informed by density functional theory.On the basis of the corresponding extended ab initio data set,we construct interpolation formulas covering the range from low-density,high-temperature to high-density,low-temperature plasmas.Our conductivity model repro-duces the well-known limits of the Spitzer and Ziman theory.We compare with available experimental data andfind very good agreement.The new conductivity model can be applied,for example,in dynamo simulations for magneticfield generation in gas giant planets,brown dwarfs,and stellar envelopes.
文摘In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2]. namely an interpolation formula of the difference of higher order. Finally we give their applications.
基金Supported by National Key Research and Development Program of China(2021YFA1601300)Young Scientists in Basic Research(YSBR-099)from Chinese Academy of Sciencesthe Postdoctoral Special Foundation of Gansu Province。
文摘We investigate the process of lepton-number-violating pion decay,which dominates the nuclear neutrinoless double beta decay induced by the short-range operator within the type-Ⅰ seesaw mechanism.The type-Ⅰ seesaw mechanism leads to the Dirac and Majorana mass terms of neutrinos by introducing the gauge-singlet righthanded neutrinos,which are often called sterile neutrinos.Applying the chiral perturbation theory,we calculate the transition amplitudes for light and heavy sterile neutrinos up to O(Q^(2)/Λ_(χ)^(2)),where Q is the typical low-energy scale in this process and Λ_(χ) the chiral symmetry breaking scale.We then adopt a naive interpolation formula of mass dependence to obtain the amplitude in the full mass range and briefly discuss its validity.
基金Supported by Shanghai Natural Science Foundation (Grant No.10ZR1410900)Key Disciplines of Shanghai Mu-nicipality (Grant No.S30104)+1 种基金the Anhui Provincial Natural Science Foundation (Grant No.070416227)Stu-dents’ Innovation Foundation of Hefei University of Technology (Grant No.XS08079)
文摘At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.
基金This work is supported in part by a grant (No.19931030) from the National Natural Science Foundation of China
文摘By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of interpolation formulae are obtained by adopting different approximate methods, to try to enhance the accuracy of the interpolatory operator. A theoretical study proves the two-level convergence of these Gauss-Seidel-type MG methods. A series of numerical experiments is presented to evaluate the relative performance of the methods with respect to the convergence factor, CPU-time(for one V-cycle and the setup phase) and computational complexity.
基金supported by the MathWorks,Inc.,King Abdullah University of Science and Technology (KAUST) (Award No. KUK-C1-013-04)the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC (Grant Agreement No. 291068)
文摘Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators.We begin by describing Chebfun's fast capabilities for Clenshaw-Curtis and also Gauss-Legendre,-Jacobi,-Hermite,and-Laguerre quadrature,based on algorithms of Waldvogel and Glaser,Liu and Rokhlin.Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles,fractional derivatives and integrals,functions defined on unbounded intervals,and the fast computation of weights for barycentric interpolation.
基金the National Natural Science Foundation of China （No. 60473114） the Natural Science Foundation of Auhui Province （No. 070416227）+2 种基金 the Natural Science Research Scheme of Education Department of Anhui Province （No. KJ2008B246） Colleges and Universities in Anhui Province Young Teachers Subsidy Scheme （No. 2008jq1110） the Science Research Foundation of Chaohu College （No. XLY-200705）.
文摘In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.
基金the startup and UPAR grants funded by College of Engineering at United Arab Emirates University(UAEU).The grant codes are G00003527 and G00004562.
文摘This paper presents new methods for spacecraft relative pose estimation using the Unscented Kalman Filter(UKF),taking into account non-additive process and measurement noises.A twistor model is employed to represent the spacecraft's relative 6-DOF motion of the chaser with respect to the target,expressed in the chaser body frame.The twistor model utilizes Modified Rodrigues Parameters(MRPs)to represent attitude with a minimal number of parameters,eliminating the need for the normalization constraint that exists in the quaternion-based model.Additionally,it incorporates both relative position and attitude in a single model,addressing kinematic coupling of states and simplifying the estimator design.Despite numerous existing pose estimation algorithms,many rely on the simplification of additive noise assumptions.This work enhances the robustness and improves the convergence of non-additive noise algorithms by deriving two methods to accurately approximate process and measurement noise covariance matrices for systems with non-additive noises.The first method utilizes the Stirling Interpolation Formula(SIF)to obtain equivalent process and measurement noise covariance matrices.The second method employs State Noise Compensation(SNC)to derive the equivalent process noise covariance matrix and uses SIF to compute the equivalent measurement noise covariance matrix.These methods are integrated into the UKF framework for estimating the relative pose of spacecraft in proximity operations,demonstrated through two scenarios:one with a cooperative target using Position Sensing Diodes(PSDs)and another with an uncooperative target using LiDAR for 3-D imaging.The effectiveness of these methods is validated against others in the literature through Monte Carlo simulations,showcasing their faster convergence and robust performance.
