This paper presents a geometric Gaussian Kaczmarz (GGK) method for solving the large-scaled consistent linear systems of equation. The GGK method improves the geometric probability randomized Kaczmarz method in <a ...This paper presents a geometric Gaussian Kaczmarz (GGK) method for solving the large-scaled consistent linear systems of equation. The GGK method improves the geometric probability randomized Kaczmarz method in <a href="#ref1">[1]</a> by introducing a new block set strategy and the iteration process. The GGK is proved to be of linear convergence. Several numerical examples show the efficiency and effectiveness of the GGK method.展开更多
A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empir...A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empirical wavelet coefficients as obtained by wavelet transformation of the data which is observed with noise. Moreover, the consistence of the test is proved while the rate of convergence is given. The method turns out to be effective after being tested on simulated examples and applied to IBM stock market data.展开更多
This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential o...This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential operators. A posteriori error estimates are discussed in context with local approximations in higher order scalar product spaces. A posteriori error computational framework (without the knowledge of theoretical solution) is presented for all BVPs regardless of the method of approximation employed in constructing the integral form. This enables computations of local errors as well as the global errors in the computed finite element solutions. The two most significant and essential aspects of the research presented in this paper that enable all of the features described above are: 1) ensuring variational consistency of the integral form(s) resulting from the methods of approximation for self adjoint, non-self adjoint, and nonlinear differential operators and 2) choosing local approximations for the elements of a discretization in a subspace of a higher order scalar product space that is minimally conforming, hence ensuring desired global differentiability of the approximations over the discretizations. It is shown that when the theoretical solution of a BVP is analytic, the a priori error estimate (in the asymptotic range, discussed in a later section of the paper) is independent of the method of approximation or the nature of the differential operator provided the resulting integral form is variationally consistent. Thus, the finite element processes utilizing integral forms based on different methods of approximation but resulting in VC integral forms result in the same a priori error estimate and convergence rate. It is shown that a variationally consistent (VC) integral form has best approximation property in some norm, conversely an integral form with best approximation property in some norm is variationally consistent. That is best approximation property of the integral form and the VC of the inte展开更多
This paper studies two multi-period mean-variance investment problems for a DC pension member before and after retirement.At any time,the pension manager can invest in a risk-free asset and multi-risky assets.Before r...This paper studies two multi-period mean-variance investment problems for a DC pension member before and after retirement.At any time,the pension manager can invest in a risk-free asset and multi-risky assets.Before retirement,the manager tries to optimize the mean-variance utility of the wealth in the member’s pension account at retirement.At retirement,the pension account wealth(or part of it)is used to purchase a paid-up annuity.After retirement,the manager has to pay the guaranteed annuity,continues to invest,and aims to optimize the mean-variance utility of the terminal wealth at a fix future time,to satisfy the pension member’s heritage and life needs in the next stage.Interest rate risk and income risk are introduced.Applying the game theory and the extended Bellman equation,the time-consistent investment strategies and the efficient frontiers before and after retirement are obtained explicitly.Obtained results indicate that the stochastic interest rate and the stochastic income have essential effects on the investment strategies.展开更多
The compressible Rayleigh-Taylor instability of accelerated ablation front is analysed in consideration of the preheat effects, and the corresponding eigen-problem is solved numerically using the fourth-order accurate...The compressible Rayleigh-Taylor instability of accelerated ablation front is analysed in consideration of the preheat effects, and the corresponding eigen-problem is solved numerically using the fourth-order accurate two- point compact difference scheme. Both the growth rate and perturbation profiles are obtained, and the obtained growth rate is close to the results of direct numerical simulation. Our results show that the growth rate is more reduced and the cutoff wave length becomes longer as preheat increases.展开更多
文摘This paper presents a geometric Gaussian Kaczmarz (GGK) method for solving the large-scaled consistent linear systems of equation. The GGK method improves the geometric probability randomized Kaczmarz method in <a href="#ref1">[1]</a> by introducing a new block set strategy and the iteration process. The GGK is proved to be of linear convergence. Several numerical examples show the efficiency and effectiveness of the GGK method.
基金the National Natural Science Foundation of China （No. 60375003） the Astronautics Basal Science Foundation of China （No. 03153059）.
文摘A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empirical wavelet coefficients as obtained by wavelet transformation of the data which is observed with noise. Moreover, the consistence of the test is proved while the rate of convergence is given. The method turns out to be effective after being tested on simulated examples and applied to IBM stock market data.
文摘This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential operators. A posteriori error estimates are discussed in context with local approximations in higher order scalar product spaces. A posteriori error computational framework (without the knowledge of theoretical solution) is presented for all BVPs regardless of the method of approximation employed in constructing the integral form. This enables computations of local errors as well as the global errors in the computed finite element solutions. The two most significant and essential aspects of the research presented in this paper that enable all of the features described above are: 1) ensuring variational consistency of the integral form(s) resulting from the methods of approximation for self adjoint, non-self adjoint, and nonlinear differential operators and 2) choosing local approximations for the elements of a discretization in a subspace of a higher order scalar product space that is minimally conforming, hence ensuring desired global differentiability of the approximations over the discretizations. It is shown that when the theoretical solution of a BVP is analytic, the a priori error estimate (in the asymptotic range, discussed in a later section of the paper) is independent of the method of approximation or the nature of the differential operator provided the resulting integral form is variationally consistent. Thus, the finite element processes utilizing integral forms based on different methods of approximation but resulting in VC integral forms result in the same a priori error estimate and convergence rate. It is shown that a variationally consistent (VC) integral form has best approximation property in some norm, conversely an integral form with best approximation property in some norm is variationally consistent. That is best approximation property of the integral form and the VC of the inte
基金supported by the National Natural Science Foundation of China(Nos.71991474,71721001 and 72001219).
文摘This paper studies two multi-period mean-variance investment problems for a DC pension member before and after retirement.At any time,the pension manager can invest in a risk-free asset and multi-risky assets.Before retirement,the manager tries to optimize the mean-variance utility of the wealth in the member’s pension account at retirement.At retirement,the pension account wealth(or part of it)is used to purchase a paid-up annuity.After retirement,the manager has to pay the guaranteed annuity,continues to invest,and aims to optimize the mean-variance utility of the terminal wealth at a fix future time,to satisfy the pension member’s heritage and life needs in the next stage.Interest rate risk and income risk are introduced.Applying the game theory and the extended Bellman equation,the time-consistent investment strategies and the efficient frontiers before and after retirement are obtained explicitly.Obtained results indicate that the stochastic interest rate and the stochastic income have essential effects on the investment strategies.
文摘The compressible Rayleigh-Taylor instability of accelerated ablation front is analysed in consideration of the preheat effects, and the corresponding eigen-problem is solved numerically using the fourth-order accurate two- point compact difference scheme. Both the growth rate and perturbation profiles are obtained, and the obtained growth rate is close to the results of direct numerical simulation. Our results show that the growth rate is more reduced and the cutoff wave length becomes longer as preheat increases.
