Based on the existing continuous borehole strain observation,the multiquadric function fitting method was used to deal with time series data. The impact of difference kernel function parameters was discussed to obtain...Based on the existing continuous borehole strain observation,the multiquadric function fitting method was used to deal with time series data. The impact of difference kernel function parameters was discussed to obtain a valuable fitting result,from which the physical connotation of the original data and its possible applications were analyzed.Meanwhile,a brief comparison was made between the results of multiquadric function fitting and polynomial fitting.展开更多
This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimiz...This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.展开更多
Price prediction plays a crucial role in portfolio selection (PS). However, most price prediction strategies only make a single prediction and do not have efficient mechanisms to make a comprehensive price prediction....Price prediction plays a crucial role in portfolio selection (PS). However, most price prediction strategies only make a single prediction and do not have efficient mechanisms to make a comprehensive price prediction. Here, we propose a comprehensive price prediction (CPP) system based on inverse multiquadrics (IMQ) radial basis function. First, the novel radial basis function (RBF) system based on IMQ function rather than traditional Gaussian (GA) function is proposed and centers on multiple price prediction strategies, aiming at improving the efficiency and robustness of price prediction. Under the novel RBF system, we then create a portfolio update strategy based on kernel and trace operator. To assess the system performance, extensive experiments are performed based on 4 data sets from different real-world financial markets. Interestingly, the experimental results reveal that the novel RBF system effectively realizes the integration of different strategies and CPP system outperforms other systems in investing performance and risk control, even considering a certain degree of transaction costs. Besides, CPP can calculate quickly, making it applicable for large-scale and time-limited financial market.展开更多
Geologic surface approximation is profoundly affected by the presence, density and location of scattered geologic input data. Many studies have recognized the importance of utilizing varied sources of information when...Geologic surface approximation is profoundly affected by the presence, density and location of scattered geologic input data. Many studies have recognized the importance of utilizing varied sources of information when reconstructing a surface. This paper presents an improved geologic surface approximation method using a multiquadric function and borehole data. Additional information, i.e., inequality elevation and dip-strikes data extracted from outcrops or mining faces, is introduced in the form of physical constraints that control local changes in the estimated surface. Commonly accepted hypothesis states that geologic surfaces can be approximated to any desired degree of exactness by the summation of regular, mathematically defined, surfaces: in particular displaced quadric forms. The coefficients of the multiquadric functions are traditionally found by a least squares method. The addition of physical constraints in this work makes such an approach into a non-deterministic polynomial time problem. Hence we propose an objective function that represents the quality of the estimated surface and that includes the additional constraints by incorporation of a penalty function. Maximizing the smoothness of the estimated surface and its fitness to the additional constraints then allows the coefficients of the multiquadric function to be obtained by iterative methods. This method was implemented and demonstrated using data collected from the 81'st coal mining area of the Huaibei Coal Group.展开更多
We solve numerically an eigenvalue elliptic partial differential equation(PDE)ranging from two to six dimensions using the generalized multiquadric(GMQ)radial basis functions(RBFs).Two discretization methods are em-pl...We solve numerically an eigenvalue elliptic partial differential equation(PDE)ranging from two to six dimensions using the generalized multiquadric(GMQ)radial basis functions(RBFs).Two discretization methods are em-ployed.The first method is similar to the classic mesh-based discretization method requiring n centers per dimension or a total ndpoints.The second method is based upon n randomly generated points in dℜrequiring far fewer data centers than the classic mesh method.Instead of having a crisp boundary,we form a“fuzzy”boundary.Using the analytic or numerical in-verse interior and boundary operators,we find the local and global minima and maxima to cull discretization points.We also find that the GMQ-RBF“flatness”can be controlled by increasing the GMQ exponential,β.We per-form a search to find the smallest root mean squared error(RMSE)by varying the exponent,the maximum,the minimum range of the GMQ shape parame-ter,and boundary influence,with the exponential having the most influence.Because the GMQ-RBFs are essentially nonlinear,it follows that the starting point of the simple search influences the end result.The optimal algorithm for high dimensional PDEs is still the subject of much research and may wait for the common place availability of massively parallel quantum computers for even higher dimensional PDEs and integral equations(IEs).展开更多
In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can ...In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of lo- cation points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly im- proved which is consistent with the theoretical results.展开更多
基金sponsored by the Annual Earthquake Tracking Task,CEA(2017010214)
文摘Based on the existing continuous borehole strain observation,the multiquadric function fitting method was used to deal with time series data. The impact of difference kernel function parameters was discussed to obtain a valuable fitting result,from which the physical connotation of the original data and its possible applications were analyzed.Meanwhile,a brief comparison was made between the results of multiquadric function fitting and polynomial fitting.
文摘This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.
文摘Price prediction plays a crucial role in portfolio selection (PS). However, most price prediction strategies only make a single prediction and do not have efficient mechanisms to make a comprehensive price prediction. Here, we propose a comprehensive price prediction (CPP) system based on inverse multiquadrics (IMQ) radial basis function. First, the novel radial basis function (RBF) system based on IMQ function rather than traditional Gaussian (GA) function is proposed and centers on multiple price prediction strategies, aiming at improving the efficiency and robustness of price prediction. Under the novel RBF system, we then create a portfolio update strategy based on kernel and trace operator. To assess the system performance, extensive experiments are performed based on 4 data sets from different real-world financial markets. Interestingly, the experimental results reveal that the novel RBF system effectively realizes the integration of different strategies and CPP system outperforms other systems in investing performance and risk control, even considering a certain degree of transaction costs. Besides, CPP can calculate quickly, making it applicable for large-scale and time-limited financial market.
基金provided by the National Science and Technology Major Project of China (Nos.2009ZX05039-004 and 2009ZX 05039-002)the National Natural Science Foundation of China (Nos.40771167 and 70621001)
文摘Geologic surface approximation is profoundly affected by the presence, density and location of scattered geologic input data. Many studies have recognized the importance of utilizing varied sources of information when reconstructing a surface. This paper presents an improved geologic surface approximation method using a multiquadric function and borehole data. Additional information, i.e., inequality elevation and dip-strikes data extracted from outcrops or mining faces, is introduced in the form of physical constraints that control local changes in the estimated surface. Commonly accepted hypothesis states that geologic surfaces can be approximated to any desired degree of exactness by the summation of regular, mathematically defined, surfaces: in particular displaced quadric forms. The coefficients of the multiquadric functions are traditionally found by a least squares method. The addition of physical constraints in this work makes such an approach into a non-deterministic polynomial time problem. Hence we propose an objective function that represents the quality of the estimated surface and that includes the additional constraints by incorporation of a penalty function. Maximizing the smoothness of the estimated surface and its fitness to the additional constraints then allows the coefficients of the multiquadric function to be obtained by iterative methods. This method was implemented and demonstrated using data collected from the 81'st coal mining area of the Huaibei Coal Group.
文摘We solve numerically an eigenvalue elliptic partial differential equation(PDE)ranging from two to six dimensions using the generalized multiquadric(GMQ)radial basis functions(RBFs).Two discretization methods are em-ployed.The first method is similar to the classic mesh-based discretization method requiring n centers per dimension or a total ndpoints.The second method is based upon n randomly generated points in dℜrequiring far fewer data centers than the classic mesh method.Instead of having a crisp boundary,we form a“fuzzy”boundary.Using the analytic or numerical in-verse interior and boundary operators,we find the local and global minima and maxima to cull discretization points.We also find that the GMQ-RBF“flatness”can be controlled by increasing the GMQ exponential,β.We per-form a search to find the smallest root mean squared error(RMSE)by varying the exponent,the maximum,the minimum range of the GMQ shape parame-ter,and boundary influence,with the exponential having the most influence.Because the GMQ-RBFs are essentially nonlinear,it follows that the starting point of the simple search influences the end result.The optimal algorithm for high dimensional PDEs is still the subject of much research and may wait for the common place availability of massively parallel quantum computers for even higher dimensional PDEs and integral equations(IEs).
文摘In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of lo- cation points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly im- proved which is consistent with the theoretical results.
