This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. N...This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency.展开更多
In this paper we present some results connected with still open problem of Gauss, negative Pell’s equation and some type graphs.In particular we prove in the Theorem 1 that all real quadratic fields K=Q( ) , generate...In this paper we present some results connected with still open problem of Gauss, negative Pell’s equation and some type graphs.In particular we prove in the Theorem 1 that all real quadratic fields K=Q( ) , generated by Fermat’s numbers with d=Fm+1=22m+1+1,m≥2, have not unique factorization. Theorem 2 give a connection of the Gauss problem with primitive Pythagorean triples. Moreover, in final part of our paper we indicate on some connections of the Gauss problem with odd graphs investigated by Cremona and Odoni in the papper [5].展开更多
For the linear least squares problem with coefficient matrix columns being highly correlated, we develop a greedy randomized Gauss-Seidel method with oblique direction. Then the corresponding convergence result is ded...For the linear least squares problem with coefficient matrix columns being highly correlated, we develop a greedy randomized Gauss-Seidel method with oblique direction. Then the corresponding convergence result is deduced. Numerical examples demonstrate that our proposed method is superior to the greedy randomized Gauss-Seidel method and the randomized Gauss-Seidel method with oblique direction.展开更多
We prove a generalized Gauss-Kuzmin-L′evy theorem for the generalized Gauss transformation Tp（x） = {p/x}.In addition, we give an estimate for the constant that appears in the theorem.
An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approx...An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approximation method.The linear part was written as a controllable canonical form to circumvent the high order time-derivative of the input and output(I/O) signals,which could multiply the measurement noise in the identification procession.Furthermore,an output error minimization was constructed for the CT Hammerstein model identification,which was then transcribed into a nonlinear programming(NLP) problem by AGPM.AGPM could converge to the true values of the CT Hammerstein model with few interpolated Legendre-Gauss(LG) nodes.Lastly,two illustrative examples were proposed to verify the accuracy and efficiency of the method.展开更多
基金supported by the National Natural Science Foundation of China(No.11171227)the Ph.D.Programs Foundation of Ministry of Education of China(No.20080270001)+2 种基金the Shanghai Leading Academic Discipline Project(No.S30405)the Fund for E-Institute of Shanghai Universities(No.E03004)the Foundation for Distinguished Young Talents in Higher Education of Guangdong of China(No.LYM09138)
文摘This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency.
文摘In this paper we present some results connected with still open problem of Gauss, negative Pell’s equation and some type graphs.In particular we prove in the Theorem 1 that all real quadratic fields K=Q( ) , generated by Fermat’s numbers with d=Fm+1=22m+1+1,m≥2, have not unique factorization. Theorem 2 give a connection of the Gauss problem with primitive Pythagorean triples. Moreover, in final part of our paper we indicate on some connections of the Gauss problem with odd graphs investigated by Cremona and Odoni in the papper [5].
文摘For the linear least squares problem with coefficient matrix columns being highly correlated, we develop a greedy randomized Gauss-Seidel method with oblique direction. Then the corresponding convergence result is deduced. Numerical examples demonstrate that our proposed method is superior to the greedy randomized Gauss-Seidel method and the randomized Gauss-Seidel method with oblique direction.
文摘We prove a generalized Gauss-Kuzmin-L′evy theorem for the generalized Gauss transformation Tp（x） = {p/x}.In addition, we give an estimate for the constant that appears in the theorem.
文摘An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approximation method.The linear part was written as a controllable canonical form to circumvent the high order time-derivative of the input and output(I/O) signals,which could multiply the measurement noise in the identification procession.Furthermore,an output error minimization was constructed for the CT Hammerstein model identification,which was then transcribed into a nonlinear programming(NLP) problem by AGPM.AGPM could converge to the true values of the CT Hammerstein model with few interpolated Legendre-Gauss(LG) nodes.Lastly,two illustrative examples were proposed to verify the accuracy and efficiency of the method.
