In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
The support vector machine (SVM) is a novel machine learning method, which has the ability to approximate nonlinear functions with arbitrary accuracy. Setting parameters well is very crucial for SVM learning results...The support vector machine (SVM) is a novel machine learning method, which has the ability to approximate nonlinear functions with arbitrary accuracy. Setting parameters well is very crucial for SVM learning results and generalization ability, and now there is no systematic, general method for parameter selection. In this article, the SVM parameter selection for function approximation is regarded as a compound optimization problem and a mutative scale chaos optimization algorithm is employed to search for optimal paraxneter values. The chaos optimization algorithm is an effective way for global optimal and the mutative scale chaos algorithm could improve the search efficiency and accuracy. Several simulation examples show the sensitivity of the SVM parameters and demonstrate the superiority of this proposed method for nonlinear function approximation.展开更多
A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In th...A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization (PSO). The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.展开更多
To study the problem of knowledge translation in fuzzy approximation spaces, the concept of rough communication of crisp set in fuzzy approximation spaces is proposed. In a rough communication of crisp set in fuzzy ap...To study the problem of knowledge translation in fuzzy approximation spaces, the concept of rough communication of crisp set in fuzzy approximation spaces is proposed. In a rough communication of crisp set in fuzzy approximation spaces, the problem of uncertainty exists, for each agent has a different language and cannot provide precise communication to each other. By means of some concepts, such as CF rough communication cut, which is a bridge between fuzzy concept and crisp concept, cut analysis of CF rough communication is made, and the relation theorem between CF rough communication and rough communication of crisp concept is obtained. Finally, in order to give an intuitive analysis of the relation between CF rough communication and rough communication of crisp concept, an example is given.展开更多
develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties: The authors this problem. Combining...develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties: The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.展开更多
Multidisciplinary feasible method (MDF) is conventional method to multidisciplinary optimization (MDO) and well-understood by users. It reduces the dimensions of the multidisciplinary optimization problem by using the...Multidisciplinary feasible method (MDF) is conventional method to multidisciplinary optimization (MDO) and well-understood by users. It reduces the dimensions of the multidisciplinary optimization problem by using the design variables as independent optimization variables. However, at each iteration of the conventional optimization procedure, multidisciplinary analysis (MDA) is numerously performed that results in extreme expense and low optimization efficiency. The intrinsic weakness of MDF is due to the times that it loop fixed-point iterations in MDA, which drive us to improve MDF by building inexpensive approximations as surrogates for expensive MDA. An simple example is presented to demonstrate the usefulness of the improved MDF. Results show that a significant reduction in the number of multidisciplinary analysis required for optimization is obtained as compared with original MDF and the efficiency of optimization is increased.展开更多
A new tight frame called as monoscale orthonormal ridgelet frame (MORF) is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to...A new tight frame called as monoscale orthonormal ridgelet frame (MORF) is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to evaluate the order of nonlinear approximation for image with edge. Because the new tight frame not only has directionality but also bears orthonormality. It overcomes redundancy of Candes's monoscale ridgelets and provides many excellent properties in practical application. Theoretical analysis and experiments demonstrate that the new frame has remarkable potential for image compression, image reconstruction, and image denoising with the simple refinement for MORF.展开更多
A simple and effective greedy algorithm for image approximation is proposed. Based on the matching pursuit approach, it is characterized by a reduced computational complexity benefiting from two major modifications. F...A simple and effective greedy algorithm for image approximation is proposed. Based on the matching pursuit approach, it is characterized by a reduced computational complexity benefiting from two major modifications. First, it iteratively finds an approximation by selecting M atoms instead of one at a time. Second, the inner product computations are confined within only a fraction of dictionary atoms at each iteration. The modifications are implemented very efficiently due to the spatial incoherence of the dictionary. Experimental results show that compared with full search matching pursuit, the proposed algorithm achieves a speed-up gain of 14.4-36.7 times while maintaining the approximation quality.展开更多
A numerical triangulation and transformation into the time domain of a Kirchhoff approximation(KA)method is proposed for the modeling of bistatic scattering from an underwater non-penetrable target.The time domain sol...A numerical triangulation and transformation into the time domain of a Kirchhoff approximation(KA)method is proposed for the modeling of bistatic scattering from an underwater non-penetrable target.The time domain solution in this approximation can be split up into two parts:the solution of reflected field,contributing around the specular direction,and the solution of shadow radiation,contributing around the forward direction.An average solution in the time domain satisfying the reciprocity principle is presented.The solution is expressed in terms of non-singular functions.The proposed method is validated against a normal mode method for bistatic scattering from a rigid sphere.Moreover,the reflected and shadow highlights on the surface of the sphere are shown to verify the integration surface of the reflected field and shadow radiation.It is also tested against a finite element method and an experiment involving a scaled Benchmark Target Strength Simulation Submarine model.The time-angle bistatic spectra for the model are evaluated by the direct and transformed average solutions of KA,and the former accelerates its speed of calculation.The results are good,and show that this method can be used to predict the bistatic scattered field of a non-penetrable target.展开更多
In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which th...In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression.展开更多
Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit (PCP). This paper exploits the higher-order generalization of matrix recovery, named higher-order princip...Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit (PCP). This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit (HOPCP), since it is critical in multi-way data analysis. Unlike the convexification (nuclear norm) for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme: the augmented Lagrangian alternating direction method (ALADM) and its truncated higher-order singular value decomposition (ALADM-THOSVD) version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.展开更多
We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,i...We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,is semantically superior for interpreting rule induction and is closely related to granularity switching in granular computing.Numerical measures about the accuracy and quality of approximations are examined.Several semantics difficulties are commented.展开更多
P k |fix| C max problem is a new scheduling problem based on the multiprocessor parallel job, and it is proved to be NP hard problem when k ≥3. This paper focuses on the case of k =3. Some new observations and new te...P k |fix| C max problem is a new scheduling problem based on the multiprocessor parallel job, and it is proved to be NP hard problem when k ≥3. This paper focuses on the case of k =3. Some new observations and new techniques for P 3 |fix| C max problem are offered. The concept of semi normal schedulings is introduced, and a very simple linear time algorithm Semi normal Algorithm for constructing semi normal schedulings is developed. With the method of the classical Graham List Scheduling, a thorough analysis of the optimal scheduling on a special instance is provided, which shows that the algorithm is an approximation algorithm of ratio of 9/8 for any instance of P 3|fix| C max problem, and improves the previous best ratio of 7/6 by M.X.Goemans.展开更多
In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potentia...In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.展开更多
This paper presents the Approximate Incrtial Manifold ∑ and its successive approximate incrtial manifold ∑i and ∑ij . We give the estimates of thickness of neighborhood of ∑, ∑j, Ejt respectively in which the eve...This paper presents the Approximate Incrtial Manifold ∑ and its successive approximate incrtial manifold ∑i and ∑ij . We give the estimates of thickness of neighborhood of ∑, ∑j, Ejt respectively in which the every solution of Navier-Stokcs equation enters.Another part of this paper presents construction method for A.I.M. by multilevel finite clement method and give error estimates of the approximate solution of incrtial form.展开更多
The second-order small slope approximation (SSA2) method is introduced to study the Doppler characteristics from time-evolving sea surfaces. Simulation results show better agreement between the SSA2 model and the nu...The second-order small slope approximation (SSA2) method is introduced to study the Doppler characteristics from time-evolving sea surfaces. Simulation results show better agreement between the SSA2 model and the numerical method for both vertical and horizontal polarizations, meaning that SSA2 gives a satisfactory prediction of the spectral difference between two po- larizations; while such discrepancy cannot be captured using the lowest-order SSA (SSA1) model. In particular, the Doppler shifts and spectral widths for different incident angles, wind directions and polarizations are analyzed, demonstrating correct variations with respect to such parameters. Those observations prove that the SSA2 provides an efficient and relatively fast tool for sea surface Doppler spectral analysis.展开更多
This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ab...This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.展开更多
High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms...High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, the approximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modified CORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to be with a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finite register length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practical applications.展开更多
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
基金the National Nature Science Foundation of China (60775047, 60402024)
文摘The support vector machine (SVM) is a novel machine learning method, which has the ability to approximate nonlinear functions with arbitrary accuracy. Setting parameters well is very crucial for SVM learning results and generalization ability, and now there is no systematic, general method for parameter selection. In this article, the SVM parameter selection for function approximation is regarded as a compound optimization problem and a mutative scale chaos optimization algorithm is employed to search for optimal paraxneter values. The chaos optimization algorithm is an effective way for global optimal and the mutative scale chaos algorithm could improve the search efficiency and accuracy. Several simulation examples show the sensitivity of the SVM parameters and demonstrate the superiority of this proposed method for nonlinear function approximation.
基金supported by the National Natural Science Foundation of China (10872030)
文摘A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization (PSO). The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.
基金supported by the Natural Science Foundation of Shandong Province (Y2006A12)the Scientific Research Development Project of Shandong Provincial Education Department (J06P01)+2 种基金the Science and Technology Foundation of Universityof Jinan (XKY0808 XKY0703)the Doctoral Foundation of University of Jinan (B0633).
文摘To study the problem of knowledge translation in fuzzy approximation spaces, the concept of rough communication of crisp set in fuzzy approximation spaces is proposed. In a rough communication of crisp set in fuzzy approximation spaces, the problem of uncertainty exists, for each agent has a different language and cannot provide precise communication to each other. By means of some concepts, such as CF rough communication cut, which is a bridge between fuzzy concept and crisp concept, cut analysis of CF rough communication is made, and the relation theorem between CF rough communication and rough communication of crisp concept is obtained. Finally, in order to give an intuitive analysis of the relation between CF rough communication and rough communication of crisp concept, an example is given.
基金supported by the National Natural Science Foundation of China under Grant No.11371001
文摘develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties: The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.
文摘Multidisciplinary feasible method (MDF) is conventional method to multidisciplinary optimization (MDO) and well-understood by users. It reduces the dimensions of the multidisciplinary optimization problem by using the design variables as independent optimization variables. However, at each iteration of the conventional optimization procedure, multidisciplinary analysis (MDA) is numerously performed that results in extreme expense and low optimization efficiency. The intrinsic weakness of MDF is due to the times that it loop fixed-point iterations in MDA, which drive us to improve MDF by building inexpensive approximations as surrogates for expensive MDA. An simple example is presented to demonstrate the usefulness of the improved MDF. Results show that a significant reduction in the number of multidisciplinary analysis required for optimization is obtained as compared with original MDF and the efficiency of optimization is increased.
基金This project was supported by the National Nature Science Foundation of China (60473119)
文摘A new tight frame called as monoscale orthonormal ridgelet frame (MORF) is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to evaluate the order of nonlinear approximation for image with edge. Because the new tight frame not only has directionality but also bears orthonormality. It overcomes redundancy of Candes's monoscale ridgelets and provides many excellent properties in practical application. Theoretical analysis and experiments demonstrate that the new frame has remarkable potential for image compression, image reconstruction, and image denoising with the simple refinement for MORF.
文摘A simple and effective greedy algorithm for image approximation is proposed. Based on the matching pursuit approach, it is characterized by a reduced computational complexity benefiting from two major modifications. First, it iteratively finds an approximation by selecting M atoms instead of one at a time. Second, the inner product computations are confined within only a fraction of dictionary atoms at each iteration. The modifications are implemented very efficiently due to the spatial incoherence of the dictionary. Experimental results show that compared with full search matching pursuit, the proposed algorithm achieves a speed-up gain of 14.4-36.7 times while maintaining the approximation quality.
基金the Oceanic Interdisciplinary Program of Shanghai Jiao Tong University(project number SL2021PT108)。
文摘A numerical triangulation and transformation into the time domain of a Kirchhoff approximation(KA)method is proposed for the modeling of bistatic scattering from an underwater non-penetrable target.The time domain solution in this approximation can be split up into two parts:the solution of reflected field,contributing around the specular direction,and the solution of shadow radiation,contributing around the forward direction.An average solution in the time domain satisfying the reciprocity principle is presented.The solution is expressed in terms of non-singular functions.The proposed method is validated against a normal mode method for bistatic scattering from a rigid sphere.Moreover,the reflected and shadow highlights on the surface of the sphere are shown to verify the integration surface of the reflected field and shadow radiation.It is also tested against a finite element method and an experiment involving a scaled Benchmark Target Strength Simulation Submarine model.The time-angle bistatic spectra for the model are evaluated by the direct and transformed average solutions of KA,and the former accelerates its speed of calculation.The results are good,and show that this method can be used to predict the bistatic scattered field of a non-penetrable target.
文摘In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression.
基金supported by the National Natural Science Foundationof China(51275348)
文摘Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit (PCP). This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit (HOPCP), since it is critical in multi-way data analysis. Unlike the convexification (nuclear norm) for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme: the augmented Lagrangian alternating direction method (ALADM) and its truncated higher-order singular value decomposition (ALADM-THOSVD) version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.
文摘We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,is semantically superior for interpreting rule induction and is closely related to granularity switching in granular computing.Numerical measures about the accuracy and quality of approximations are examined.Several semantics difficulties are commented.
文摘P k |fix| C max problem is a new scheduling problem based on the multiprocessor parallel job, and it is proved to be NP hard problem when k ≥3. This paper focuses on the case of k =3. Some new observations and new techniques for P 3 |fix| C max problem are offered. The concept of semi normal schedulings is introduced, and a very simple linear time algorithm Semi normal Algorithm for constructing semi normal schedulings is developed. With the method of the classical Graham List Scheduling, a thorough analysis of the optimal scheduling on a special instance is provided, which shows that the algorithm is an approximation algorithm of ratio of 9/8 for any instance of P 3|fix| C max problem, and improves the previous best ratio of 7/6 by M.X.Goemans.
基金The project was supported by the Fund for Scientific Research in Flanders (FWO-Vlaanderen) for Research Grant G021115N.
文摘In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.
文摘This paper presents the Approximate Incrtial Manifold ∑ and its successive approximate incrtial manifold ∑i and ∑ij . We give the estimates of thickness of neighborhood of ∑, ∑j, Ejt respectively in which the every solution of Navier-Stokcs equation enters.Another part of this paper presents construction method for A.I.M. by multilevel finite clement method and give error estimates of the approximate solution of incrtial form.
基金supported by the National Natural Science Foundation of China (40771133)
文摘The second-order small slope approximation (SSA2) method is introduced to study the Doppler characteristics from time-evolving sea surfaces. Simulation results show better agreement between the SSA2 model and the numerical method for both vertical and horizontal polarizations, meaning that SSA2 gives a satisfactory prediction of the spectral difference between two po- larizations; while such discrepancy cannot be captured using the lowest-order SSA (SSA1) model. In particular, the Doppler shifts and spectral widths for different incident angles, wind directions and polarizations are analyzed, demonstrating correct variations with respect to such parameters. Those observations prove that the SSA2 provides an efficient and relatively fast tool for sea surface Doppler spectral analysis.
文摘This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.
基金This project was supported by the Natural Science Foundation of Shaanxi Province.
文摘High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, the approximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modified CORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to be with a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finite register length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practical applications.