In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only o...In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only one evaluation of its derivative are constructed by the inverse interpolation with the memory on the previous step for solving the simple root of a nonlinear equation. The order and order of convergence of them are proved respectively. Finally, the proposed methods and the basins of attraction are demonstrated by the numerical examples.展开更多
Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P&...Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +展开更多
A convenient numerical calculation method (inverse spline interpolation) for all-time apparent resistivity intransient electromagnetic method (TEM) is proposed in this paper. Characteristic of early and late normalize...A convenient numerical calculation method (inverse spline interpolation) for all-time apparent resistivity intransient electromagnetic method (TEM) is proposed in this paper. Characteristic of early and late normalized inductiveelectromotive force was investigated. According to the turning point, the transient process is divided into the earlyphase, the turning point, and the late phase. Afterwards, apparent resistivity is obtained through inverse spline interpo-lation in the early and the late phases, respectively. Finally, the resistivities of the early-time and the late-time wereconnected together by the turning point. The result shows that the inverse spline method is feasible and the method alsolays a foundation for initial model construction in the TEM automatic inversion.展开更多
Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (...Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (DIC) algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton (IC-GN) algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.展开更多
Gravity Anomaly Correction(GAC)is a very important term in leveling data processing.In most cases,it is troublesome for field surveyors to measure gravity when leveling.In this paper,based on the complete Bouguer Grav...Gravity Anomaly Correction(GAC)is a very important term in leveling data processing.In most cases,it is troublesome for field surveyors to measure gravity when leveling.In this paper,based on the complete Bouguer Gravity Anomaly(BGA)map of WGM2012,the feasibility of replacing in-situ gravity surveying in China is investigated.For leveling application,that is to evaluate the accuracy of WGM2012 in China.Because WGM2012 is organized with a standard rectangle grid,two interpolation methods,bilinear interpolating and Inverse Distance Weighted(IDW)interpolating,are proposed.Four sample areas in China,i.e.,Hanzhong,Chengdu,Linzhi and Shantou,are selected to evaluate the systems bias and precision of WGM2012.Numerical results show the average system bias of WGM2012 BGA in west China is about-100.1 mGal(1 mGal=10^(-5) m/s^(2))and the standard deviation is about 30.7 mGal.Tests in Shantou indicate the system bias in plain areas is about-130.4 mGal and standard deviation is about 6.8 mGal.All these experiments means the accuracy of WGM2012 is limited in high mountain areas of western China,but in plain areas,such as Shantou,WGM2012 BGA map is quite good for most leveling applications after calibrating the system bias.展开更多
Based on the daily precipitation data between 1965 and 2009 from 18 rainfall stations in Guangdong Beijiang River basin and the definitions of Precipitation Concentration Degree(PCD) and Precipitation Concentration Pe...Based on the daily precipitation data between 1965 and 2009 from 18 rainfall stations in Guangdong Beijiang River basin and the definitions of Precipitation Concentration Degree(PCD) and Precipitation Concentration Period(PCP),the inhomogeneous distribution characteristics of interannual precipitation were analyzed by introducing the spatial distribution of annual mean values,variable coefficients,correlation coefficients between annual precipitation,change trends and composite analysis. The results showed that(1) PCD mainly decreased from south to north in spatial distribution; PCP was earlier in most of north-central basin,but relatively later in southern basin.(2) Annual precipitation would increase if PCD decreased in most of river basin,and annual precipitation would decrease as PCP lagged in southern basin,but the change trend was the opposite in northern basin.(3) PCD and PCP mainly showed insignificant upward trend in the entire basin by Mann-Kendall test.展开更多
Based on the daily precipitation data between 1965 and 2009 from 8 rainfall stations in Shaoguan City,the indexes of precipitation concentration degree( PCD) and precipitation concentration period( PCP) were calcu...Based on the daily precipitation data between 1965 and 2009 from 8 rainfall stations in Shaoguan City,the indexes of precipitation concentration degree( PCD) and precipitation concentration period( PCP) were calculated. And then inverse distance weighted( IDW) interpolation method was used to analyze the heterogeneous distribution characteristics of inter-annual precipitation by introducing the spatial distribution of annual mean values,variable coefficients,correlation coefficients with annual precipitation,change trends and composite analysis. The results showed that PCD was mainly decreasing from southeast to northwest in spatial distribution,long-term average annual values of PCP were distributed in the first ten days of June at most region. Annual precipitation increased as PCD increased in southern region,but the change trend was the opposite in northern region. Annual precipitation increased as PCP lagged in most region. PCD and PCP mainly appeared upward trend. Composite analysis of PCD in more-precipitation years was similar to less-precipitation years in spatial distribution,but the PCD in less-precipitation years was higher.Seen from the mean in the whole region,PCP in more-precipitation years lagged about 20 days behind those in less-precipitation years. The research can provide basis for the production of agriculture and industry as well as disaster prevention and reduction.展开更多
Quality and robustness of grid deformation is of the most importance in the field of aircraft design, and grid in high quality is essential for improving the precision of numerical simulation. In order to maintain the...Quality and robustness of grid deformation is of the most importance in the field of aircraft design, and grid in high quality is essential for improving the precision of numerical simulation. In order to maintain the orthogonality of deformed grid, the displacement of grid points is divided into rotational and translational parts in this paper, and inverse distance weighted interpolation is used to transfer the changing location from boundary grid to the spatial grid. Moreover, the deformation of rotational part is implemented in combination with the exponential space mapping that improves the certainty and stability of quaternion interpolation. Furthermore, the new grid deformation technique named ‘‘layering blend deformation'' is built based on the basic quaternion technique, which combines the layering arithmetic with transfinite interpolation(TFI) technique. Then the proposed technique is applied in the movement of airfoil, parametric modeling, and the deformation of complex configuration, in which the robustness of grid quality is tested. The results show that the new method has the capacity to deal with the problems with large deformation, and the ‘‘layering blend deformation'' improves the efficiency and quality of the basic quaternion deformation method significantly.展开更多
文摘In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only one evaluation of its derivative are constructed by the inverse interpolation with the memory on the previous step for solving the simple root of a nonlinear equation. The order and order of convergence of them are proved respectively. Finally, the proposed methods and the basins of attraction are demonstrated by the numerical examples.
文摘Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +
基金Project 40344022 supported by National Natural Science Foundation of China
文摘A convenient numerical calculation method (inverse spline interpolation) for all-time apparent resistivity intransient electromagnetic method (TEM) is proposed in this paper. Characteristic of early and late normalized inductiveelectromotive force was investigated. According to the turning point, the transient process is divided into the earlyphase, the turning point, and the late phase. Afterwards, apparent resistivity is obtained through inverse spline interpo-lation in the early and the late phases, respectively. Finally, the resistivities of the early-time and the late-time wereconnected together by the turning point. The result shows that the inverse spline method is feasible and the method alsolays a foundation for initial model construction in the TEM automatic inversion.
基金financially supported by the National Natural Science Foundation of China(11202081,11272124,and 11472109)the State Key Lab of Subtropical Building Science,South China University of Technology(2014ZC17)
文摘Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (DIC) algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton (IC-GN) algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.
基金“Wings of Quality”Program of QICS(No.2020-zlzy-015)。
文摘Gravity Anomaly Correction(GAC)is a very important term in leveling data processing.In most cases,it is troublesome for field surveyors to measure gravity when leveling.In this paper,based on the complete Bouguer Gravity Anomaly(BGA)map of WGM2012,the feasibility of replacing in-situ gravity surveying in China is investigated.For leveling application,that is to evaluate the accuracy of WGM2012 in China.Because WGM2012 is organized with a standard rectangle grid,two interpolation methods,bilinear interpolating and Inverse Distance Weighted(IDW)interpolating,are proposed.Four sample areas in China,i.e.,Hanzhong,Chengdu,Linzhi and Shantou,are selected to evaluate the systems bias and precision of WGM2012.Numerical results show the average system bias of WGM2012 BGA in west China is about-100.1 mGal(1 mGal=10^(-5) m/s^(2))and the standard deviation is about 30.7 mGal.Tests in Shantou indicate the system bias in plain areas is about-130.4 mGal and standard deviation is about 6.8 mGal.All these experiments means the accuracy of WGM2012 is limited in high mountain areas of western China,but in plain areas,such as Shantou,WGM2012 BGA map is quite good for most leveling applications after calibrating the system bias.
基金Supported by the National Natural Science Fund of China(41571091)the "13th Five-year" Planning Item of Guangdong Philosophy and Social Sciences(GD16CGL10)
文摘Based on the daily precipitation data between 1965 and 2009 from 18 rainfall stations in Guangdong Beijiang River basin and the definitions of Precipitation Concentration Degree(PCD) and Precipitation Concentration Period(PCP),the inhomogeneous distribution characteristics of interannual precipitation were analyzed by introducing the spatial distribution of annual mean values,variable coefficients,correlation coefficients between annual precipitation,change trends and composite analysis. The results showed that(1) PCD mainly decreased from south to north in spatial distribution; PCP was earlier in most of north-central basin,but relatively later in southern basin.(2) Annual precipitation would increase if PCD decreased in most of river basin,and annual precipitation would decrease as PCP lagged in southern basin,but the change trend was the opposite in northern basin.(3) PCD and PCP mainly showed insignificant upward trend in the entire basin by Mann-Kendall test.
基金Supported by the National Natural Science Fund of China(41371498,31170486,41571091)Youth Fund of Humanistic and Social Sciences of the Ministry of Education of PRC in 2017(17YJCZH114)the"13th Five-year"Planning Item of Guangdong Philosophy and Social Sciences(GD16CGL10)
文摘Based on the daily precipitation data between 1965 and 2009 from 8 rainfall stations in Shaoguan City,the indexes of precipitation concentration degree( PCD) and precipitation concentration period( PCP) were calculated. And then inverse distance weighted( IDW) interpolation method was used to analyze the heterogeneous distribution characteristics of inter-annual precipitation by introducing the spatial distribution of annual mean values,variable coefficients,correlation coefficients with annual precipitation,change trends and composite analysis. The results showed that PCD was mainly decreasing from southeast to northwest in spatial distribution,long-term average annual values of PCP were distributed in the first ten days of June at most region. Annual precipitation increased as PCD increased in southern region,but the change trend was the opposite in northern region. Annual precipitation increased as PCP lagged in most region. PCD and PCP mainly appeared upward trend. Composite analysis of PCD in more-precipitation years was similar to less-precipitation years in spatial distribution,but the PCD in less-precipitation years was higher.Seen from the mean in the whole region,PCP in more-precipitation years lagged about 20 days behind those in less-precipitation years. The research can provide basis for the production of agriculture and industry as well as disaster prevention and reduction.
文摘Quality and robustness of grid deformation is of the most importance in the field of aircraft design, and grid in high quality is essential for improving the precision of numerical simulation. In order to maintain the orthogonality of deformed grid, the displacement of grid points is divided into rotational and translational parts in this paper, and inverse distance weighted interpolation is used to transfer the changing location from boundary grid to the spatial grid. Moreover, the deformation of rotational part is implemented in combination with the exponential space mapping that improves the certainty and stability of quaternion interpolation. Furthermore, the new grid deformation technique named ‘‘layering blend deformation'' is built based on the basic quaternion technique, which combines the layering arithmetic with transfinite interpolation(TFI) technique. Then the proposed technique is applied in the movement of airfoil, parametric modeling, and the deformation of complex configuration, in which the robustness of grid quality is tested. The results show that the new method has the capacity to deal with the problems with large deformation, and the ‘‘layering blend deformation'' improves the efficiency and quality of the basic quaternion deformation method significantly.