In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches ...In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.展开更多
The diagonal Pade' approximates for exp(x). tanx and tanhx are obtained in asimple manner by using the property of Legendre polynomials that on [ -1, 1] Pn (x)is orthogonal to every polynomial of lower degree. Gau...The diagonal Pade' approximates for exp(x). tanx and tanhx are obtained in asimple manner by using the property of Legendre polynomials that on [ -1, 1] Pn (x)is orthogonal to every polynomial of lower degree. Gauss's quadrature formula is used tofined the denomiators of some functions.展开更多
In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and ...In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.展开更多
The problem of solving the linear diffusion equation by a method related to the Restrictive Pade Approximation (RPA) is considered. The advantage is that it has the exact value at certain r. This method will exhibit s...The problem of solving the linear diffusion equation by a method related to the Restrictive Pade Approximation (RPA) is considered. The advantage is that it has the exact value at certain r. This method will exhibit several advantages for example highly accurate, fast and with good results, etc. The absolutely error is still very small. The obtained results are compared with the exact solution and the other methods. The numerical results are in agreement with the exact solution.展开更多
The nomaal moveout correction is important to long-offset observations, especially deep layers. For isotropic media, the conventional two-term approximation of the normal moveout function assumes a small offset-to-dep...The nomaal moveout correction is important to long-offset observations, especially deep layers. For isotropic media, the conventional two-term approximation of the normal moveout function assumes a small offset-to-depth ratio and thus fails at large offset-to-depth ratios. We approximate the long-offset moveout using the Pade approximation. This method is superior to typical methods and flattens the seismic gathers over a wide range of offsets in multilayered media. For a four-layer model, traditional methods show traveltime errors of about 5 ms for offset-to-depth ratio of 2 and greater than 10 ms for offset-to-depth ratio of 3; in contrast, the maximum traveltime error for the [3, 3]-order Pade approximation is no more than 5 ms at offset-to-depth ratio of 3. For the Cooper Basin model, the maximum oft＇set-to-depth ratio for the [3, 3]-order Pade approximation is typically double of those in typical methods. The [7, 7]-order Pade approximation performs better than the [3.3]-order Pade armroximation.展开更多
To solve the Fredholm integral equations of the second kind, a new notion of the least-squares orthogonal polyno- mials of function-valued Pade-type approximation is introduced. On the basis of the error formula, the ...To solve the Fredholm integral equations of the second kind, a new notion of the least-squares orthogonal polyno- mials of function-valued Pade-type approximation is introduced. On the basis of the error formula, the least-squares function： valued Pad＆type approximation is constructed. Their existence and uniqueness are studied. A recursive computation formula of the least-squares function-valued Padetype approximation is given. In the end, an example is given to show that the method is effective and stable.展开更多
Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. R...Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. Rational approximations of the Laplace solutions such as the Pade approximation can be used for this purpose. For some heat conduction problems appearing in a semi-infinite slab, however, such rational approximations are not easy to obtain because the Laplace solutions are not analytic at the origin. In this article, a continued fraction method has been proposed to obtain rational approximations of such heat conduction dynamics in a semi-infinite slab.展开更多
The magnetic interface forward and inversion method is realized using the Taylor series expansion to linearize the Fourier transform of the exponential function. With a large expansion step and unbounded neighborhood,...The magnetic interface forward and inversion method is realized using the Taylor series expansion to linearize the Fourier transform of the exponential function. With a large expansion step and unbounded neighborhood, the Taylor series is not convergent, and therefore, this paper presents the magnetic interface forward and inversion method based on Pade approximation instead of the Taylor series expansion. Compared with the Taylor series, Pade＇s expansion＇s convergence is more stable and its approximation more accurate. Model tests show the validity of the magnetic forward modeling and inversion of Pade approximation proposed in the paper, and when this inversion method is applied to the measured data of the Matagami area in Canada, a stable and reasonable distribution of underground interface is obtained.展开更多
Convergence conclusions of Pade approximants in the univariate case can be found in various papers. However,resuhs in the multivariate case are few.A.Cuyt seems to be the only one who discusses convergence for multiva...Convergence conclusions of Pade approximants in the univariate case can be found in various papers. However,resuhs in the multivariate case are few.A.Cuyt seems to be the only one who discusses convergence for multivariate Pade approximants,she gives in[2]a de Montessus de Bollore type theorem.In this paper,we will discuss the zero set of a real multivariate polynomial,and present a convergence theorem in measure of multivariate Pade approximant.The proof technique used in this paper is quite different from that used in the univariate case.展开更多
An interval Pade-type approximation is introduced and then Routh-Pade-type method （IRPTM） is presented to model reduction in interval systems. The denominator in reduced model is obtained from the stable Routh table...An interval Pade-type approximation is introduced and then Routh-Pade-type method （IRPTM） is presented to model reduction in interval systems. The denominator in reduced model is obtained from the stable Routh table, and its numerator is constructed by the interval Pade-type definition. Compared to the existing Routh-Pade method, IRPTM does not need to solve linear interval equations theoretical analysis shows that IRPTM has example is given to illustrate our method. Hence, we do not have to compute smaller computational cost than that interval division in the process. Moreover, of Routh-Pade method. A typical numerical展开更多
A new vector-valued Pad′e-type approximation is defined by introducing a gener- alized vector-valued linear functional from a scalar polynomial space to a vector space. Some algebraic properties and error formulas ar...A new vector-valued Pad′e-type approximation is defined by introducing a gener- alized vector-valued linear functional from a scalar polynomial space to a vector space. Some algebraic properties and error formulas are presented. The expressions of this Pad′e-type ap- proximants are provided with the generating function form and the determinant form.展开更多
内模控制方法因具有诸多优点而引起了业界的广泛关注,但难以在DCS中直接实现,现有的IMC-PID设计方法存在着只针对特定模型才能设计或通用设计但近似程度偏低的问题,提出了一种新的IMC-PID控制器设计方法,采用一般形式的Pade多项式逼近IM...内模控制方法因具有诸多优点而引起了业界的广泛关注,但难以在DCS中直接实现,现有的IMC-PID设计方法存在着只针对特定模型才能设计或通用设计但近似程度偏低的问题,提出了一种新的IMC-PID控制器设计方法,采用一般形式的Pade多项式逼近IMC-PID转化过程中出现的复杂项,然后对照该Pade多项式和PID控制器表达式设计PID控制器参数。该方法广泛适用于各种单变量对象,也能够毫无修改地应用于多变量系统的IMC-PID控制器参数设计。与基于M ac laurin展式的IMC-PID设计方法相比,该方法提供了具有更强理论依据的微分滤波时间常数计算式,能够获得与内模策略更为接近的控制效果。展开更多
基金This research is suported by National Science foundation Grant.
文摘In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.
文摘The diagonal Pade' approximates for exp(x). tanx and tanhx are obtained in asimple manner by using the property of Legendre polynomials that on [ -1, 1] Pn (x)is orthogonal to every polynomial of lower degree. Gauss's quadrature formula is used tofined the denomiators of some functions.
文摘In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.
文摘The problem of solving the linear diffusion equation by a method related to the Restrictive Pade Approximation (RPA) is considered. The advantage is that it has the exact value at certain r. This method will exhibit several advantages for example highly accurate, fast and with good results, etc. The absolutely error is still very small. The obtained results are compared with the exact solution and the other methods. The numerical results are in agreement with the exact solution.
基金supported by the National Natural Science Foundation of China(Nos.41130418 and 41374061)the National Major Project of China(No.2011ZX05008-006)and the Youth Innovation Promotion Association CAS(No.2012054)
文摘The nomaal moveout correction is important to long-offset observations, especially deep layers. For isotropic media, the conventional two-term approximation of the normal moveout function assumes a small offset-to-depth ratio and thus fails at large offset-to-depth ratios. We approximate the long-offset moveout using the Pade approximation. This method is superior to typical methods and flattens the seismic gathers over a wide range of offsets in multilayered media. For a four-layer model, traditional methods show traveltime errors of about 5 ms for offset-to-depth ratio of 2 and greater than 10 ms for offset-to-depth ratio of 3; in contrast, the maximum traveltime error for the [3, 3]-order Pade approximation is no more than 5 ms at offset-to-depth ratio of 3. For the Cooper Basin model, the maximum oft＇set-to-depth ratio for the [3, 3]-order Pade approximation is typically double of those in typical methods. The [7, 7]-order Pade approximation performs better than the [3.3]-order Pade armroximation.
基金supported by the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘To solve the Fredholm integral equations of the second kind, a new notion of the least-squares orthogonal polyno- mials of function-valued Pade-type approximation is introduced. On the basis of the error formula, the least-squares function： valued Pad＆type approximation is constructed. Their existence and uniqueness are studied. A recursive computation formula of the least-squares function-valued Padetype approximation is given. In the end, an example is given to show that the method is effective and stable.
文摘Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. Rational approximations of the Laplace solutions such as the Pade approximation can be used for this purpose. For some heat conduction problems appearing in a semi-infinite slab, however, such rational approximations are not easy to obtain because the Laplace solutions are not analytic at the origin. In this article, a continued fraction method has been proposed to obtain rational approximations of such heat conduction dynamics in a semi-infinite slab.
基金supported by Sino Probe-09-01-Integrated geophysical data processing and integrated system for moving platform(No.201311192)Graduate innovation fund of Jilin University(No.2015025)
文摘The magnetic interface forward and inversion method is realized using the Taylor series expansion to linearize the Fourier transform of the exponential function. With a large expansion step and unbounded neighborhood, the Taylor series is not convergent, and therefore, this paper presents the magnetic interface forward and inversion method based on Pade approximation instead of the Taylor series expansion. Compared with the Taylor series, Pade＇s expansion＇s convergence is more stable and its approximation more accurate. Model tests show the validity of the magnetic forward modeling and inversion of Pade approximation proposed in the paper, and when this inversion method is applied to the measured data of the Matagami area in Canada, a stable and reasonable distribution of underground interface is obtained.
基金Supported by National Science Foundation of China for Youth
文摘Convergence conclusions of Pade approximants in the univariate case can be found in various papers. However,resuhs in the multivariate case are few.A.Cuyt seems to be the only one who discusses convergence for multivariate Pade approximants,she gives in[2]a de Montessus de Bollore type theorem.In this paper,we will discuss the zero set of a real multivariate polynomial,and present a convergence theorem in measure of multivariate Pade approximant.The proof technique used in this paper is quite different from that used in the univariate case.
基金Project supported by the National Natural Science Foundation of China (Grant No.10271074)the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘An interval Pade-type approximation is introduced and then Routh-Pade-type method （IRPTM） is presented to model reduction in interval systems. The denominator in reduced model is obtained from the stable Routh table, and its numerator is constructed by the interval Pade-type definition. Compared to the existing Routh-Pade method, IRPTM does not need to solve linear interval equations theoretical analysis shows that IRPTM has example is given to illustrate our method. Hence, we do not have to compute smaller computational cost than that interval division in the process. Moreover, of Routh-Pade method. A typical numerical
基金The work is supported by the National Natural Science Foundation of China (10271074).
文摘A new vector-valued Pad′e-type approximation is defined by introducing a gener- alized vector-valued linear functional from a scalar polynomial space to a vector space. Some algebraic properties and error formulas are presented. The expressions of this Pad′e-type ap- proximants are provided with the generating function form and the determinant form.
文摘内模控制方法因具有诸多优点而引起了业界的广泛关注,但难以在DCS中直接实现,现有的IMC-PID设计方法存在着只针对特定模型才能设计或通用设计但近似程度偏低的问题,提出了一种新的IMC-PID控制器设计方法,采用一般形式的Pade多项式逼近IMC-PID转化过程中出现的复杂项,然后对照该Pade多项式和PID控制器表达式设计PID控制器参数。该方法广泛适用于各种单变量对象,也能够毫无修改地应用于多变量系统的IMC-PID控制器参数设计。与基于M ac laurin展式的IMC-PID设计方法相比,该方法提供了具有更强理论依据的微分滤波时间常数计算式,能够获得与内模策略更为接近的控制效果。
