For the calculation of non-linear magnetic fields, a simple program can be as effective as a large commercialized software package. If relaxation methods are used, they must include successive over-relaxation and unde...For the calculation of non-linear magnetic fields, a simple program can be as effective as a large commercialized software package. If relaxation methods are used, they must include successive over-relaxation and under-relaxation and much attention must be paid to the relaxation factor and the interpolation. In this paper some skills are proposed on the setting of an interpolation switch and the choosing of saturation point so as to assure satisfied convergence properties. The numerical results by using these methods conform well to the tests.展开更多
The paper presents a new algorithm of NonLinearly Adaptive Interpolation (NLAI). NLAI is based on both the gradients and the curvature of the signals with the predicted subsection. It is characterized by adap- tive no...The paper presents a new algorithm of NonLinearly Adaptive Interpolation (NLAI). NLAI is based on both the gradients and the curvature of the signals with the predicted subsection. It is characterized by adap- tive nonlinear interpolation method with extracting the characteristics of signals. Experimental research testi- fies the validity of the algorithm using the echoes of the Ground Penetrating Radar (GPR). A comparison of this algorithm with other traditional algorithms demonstrates that it is feasible.展开更多
The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth ord...The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth order problems.展开更多
Newton interpolation and Thiele-type continued fractions interpolation may be the favoured linear interpolation and nonlinear interpolation,but these two interpolations could not solve all the interpolant problems.In ...Newton interpolation and Thiele-type continued fractions interpolation may be the favoured linear interpolation and nonlinear interpolation,but these two interpolations could not solve all the interpolant problems.In this paper,several general frames are established by introducing multiple parameters and they are extensions and improvements of those for the general frames studied by Tan and Fang.Numerical examples are given to show the effectiveness of the results in this paper.展开更多
This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvalure. The nonlinearity can be described by the curve of the solut...This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvalure. The nonlinearity can be described by the curve of the solution locus and the equal interval input of joints mapping into inequable interval output of the end-effectors. Such curing and inequation can be measured by BW curvature. So the curvature can measure the nonlinearity of PKM indirectly. Then the distribution of BW curvature in the local area and the whole workspace are also discussed. An example of application to the interpolation accuracy analysis of PKM is given to illustrate the effectiveness of this approach.展开更多
In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimen...In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.展开更多
基金Supported by the National Natural Science Fundation of China(No.69881002)
文摘For the calculation of non-linear magnetic fields, a simple program can be as effective as a large commercialized software package. If relaxation methods are used, they must include successive over-relaxation and under-relaxation and much attention must be paid to the relaxation factor and the interpolation. In this paper some skills are proposed on the setting of an interpolation switch and the choosing of saturation point so as to assure satisfied convergence properties. The numerical results by using these methods conform well to the tests.
基金Supported by the National Natural Science Foundation of China (No.60572152).
文摘The paper presents a new algorithm of NonLinearly Adaptive Interpolation (NLAI). NLAI is based on both the gradients and the curvature of the signals with the predicted subsection. It is characterized by adap- tive nonlinear interpolation method with extracting the characteristics of signals. Experimental research testi- fies the validity of the algorithm using the echoes of the Ground Penetrating Radar (GPR). A comparison of this algorithm with other traditional algorithms demonstrates that it is feasible.
文摘The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth order problems.
基金the National Natural Science Foundation of China (No.60473114)the Anhui Provincial Natural Science Foundation (No.070416227)the Key Project Foundation of the Department of Education of Anhui Province (No.KJ2008A027)
文摘Newton interpolation and Thiele-type continued fractions interpolation may be the favoured linear interpolation and nonlinear interpolation,but these two interpolations could not solve all the interpolant problems.In this paper,several general frames are established by introducing multiple parameters and they are extensions and improvements of those for the general frames studied by Tan and Fang.Numerical examples are given to show the effectiveness of the results in this paper.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 59805011) the National 973 Program (G1998030607) the National 863 High-Tech Development Program (863-511-943-001).
文摘This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvalure. The nonlinearity can be described by the curve of the solution locus and the equal interval input of joints mapping into inequable interval output of the end-effectors. Such curing and inequation can be measured by BW curvature. So the curvature can measure the nonlinearity of PKM indirectly. Then the distribution of BW curvature in the local area and the whole workspace are also discussed. An example of application to the interpolation accuracy analysis of PKM is given to illustrate the effectiveness of this approach.
基金Supported by the National Natural Science Foundation of China under Grant No. 61173050
文摘In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.
