In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establi...In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.展开更多
The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was c...The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.展开更多
In this paper, a simplified iterative regnlarization method was used to solve the operator equations of the first kind involving semi-positive definite operators, the convergence rates of regularized solutions were ob...In this paper, a simplified iterative regnlarization method was used to solve the operator equations of the first kind involving semi-positive definite operators, the convergence rates of regularized solutions were obtained and a posteriori parametr choice strategy was given.展开更多
In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution （if it exists） does not depend continuously on the data. The generalized Tikhono...In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution （if it exists） does not depend continuously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained, Numerical examples are presented to illustrate the validity and effectiveness of this method.展开更多
The effects of dilatational phase transformation on the target strength of ceramic materi- als are investigated based on Tate's model.The constitutive behavior of materials in different regions (elastic,cracked,pl...The effects of dilatational phase transformation on the target strength of ceramic materi- als are investigated based on Tate's model.The constitutive behavior of materials in different regions (elastic,cracked,plastic and phase transformation)are taken into account.It is found that,with a proper choice of material parameters,the dilatational phase transformation can increase effectively the target strength R_t.This would be of importance in penetration-resistance design.展开更多
In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the imple- mentation of Lavrentiev regularization method. ...In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the imple- mentation of Lavrentiev regularization method. Using general HSlder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock （2005） for choosing the regularization parameter.展开更多
In this paper we show a systematic method of appropriate parameter choice for a circular proton-proton collider by using an analytical expression for the beam beam tune shift limit, starting from a given design goal a...In this paper we show a systematic method of appropriate parameter choice for a circular proton-proton collider by using an analytical expression for the beam beam tune shift limit, starting from a given design goal and technical limitations. A suitable parameter space has been explored. Based on the parameter scan, sets of appropriate parameters designed for a 50 km and 100 km circular proton proton collider are proposed.展开更多
In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarant...In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ1/2) for Tikhonov-Browder regularization, where δ denotes the noise level of the data perturbation.展开更多
We propose a multiscale projection method for the numerical solution of the irtatively regularized Gauss-Newton method of nonlinear integral equations.An a posteriori rule is suggested to choose the stopping index of ...We propose a multiscale projection method for the numerical solution of the irtatively regularized Gauss-Newton method of nonlinear integral equations.An a posteriori rule is suggested to choose the stopping index of iteration and the rates of convergence are also derived under the Lipschitz condition.Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.展开更多
To reduce the computational cost,we propose a regularizing modified LevenbergMarquardt scheme via multiscale Galerkin method for solving nonlinear ill-posed problems.Convergence results for the regularizing modified L...To reduce the computational cost,we propose a regularizing modified LevenbergMarquardt scheme via multiscale Galerkin method for solving nonlinear ill-posed problems.Convergence results for the regularizing modified Levenberg-Marquardt scheme for the solution of nonlinear ill-posed problems have been proved.Based on these results,we propose a modified heuristic parameter choice rule to terminate the regularizing modified Levenberg-Marquardt scheme.By imposing certain conditions on the noise,we derive optimal convergence rates on the approximate solution under special source conditions.Numerical results are presented to illustrate the performance of the regularizing modified Levenberg-Marquardt scheme under the modified heuristic parameter choice.展开更多
基金supported by the Natural Science Foundation of China(10771017,10971015,10231030)Key Project to Ministry of Education of the People’s Republic of China(309007)
文摘In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.
文摘The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.
文摘In this paper, a simplified iterative regnlarization method was used to solve the operator equations of the first kind involving semi-positive definite operators, the convergence rates of regularized solutions were obtained and a posteriori parametr choice strategy was given.
基金supported by the National Natural Science Foundation of China(11171136, 11261032)the Distinguished Young Scholars Fund of Lan Zhou University of Technology (Q201015)the basic scientific research business expenses of Gansu province college
文摘In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution （if it exists） does not depend continuously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained, Numerical examples are presented to illustrate the validity and effectiveness of this method.
基金the Excellent Youth Foundation of Harbin Institute of Technology
文摘The effects of dilatational phase transformation on the target strength of ceramic materi- als are investigated based on Tate's model.The constitutive behavior of materials in different regions (elastic,cracked,plastic and phase transformation)are taken into account.It is found that,with a proper choice of material parameters,the dilatational phase transformation can increase effectively the target strength R_t.This would be of importance in penetration-resistance design.
基金National Institute of Technology Karnataka, India, for the financial support
文摘In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the imple- mentation of Lavrentiev regularization method. Using general HSlder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock （2005） for choosing the regularization parameter.
基金Supported by National Natural Science Foundation of China(11175192)
文摘In this paper we show a systematic method of appropriate parameter choice for a circular proton-proton collider by using an analytical expression for the beam beam tune shift limit, starting from a given design goal and technical limitations. A suitable parameter space has been explored. Based on the parameter scan, sets of appropriate parameters designed for a 50 km and 100 km circular proton proton collider are proposed.
基金Partially supported by the Young Teachers Foundation of Zhongshan University.
文摘In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ1/2) for Tikhonov-Browder regularization, where δ denotes the noise level of the data perturbation.
基金Supported in part by the Natural Science Foundation of China under grants 11761010 and 61863001.
文摘We propose a multiscale projection method for the numerical solution of the irtatively regularized Gauss-Newton method of nonlinear integral equations.An a posteriori rule is suggested to choose the stopping index of iteration and the rates of convergence are also derived under the Lipschitz condition.Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.
基金Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(2020B1212060032)Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques(400440)+1 种基金the Foundation of Education Committee of Jiangxi,China(GJJ201436)National Natural Science Foundation of China under grants 11571386 and 11761010.
文摘To reduce the computational cost,we propose a regularizing modified LevenbergMarquardt scheme via multiscale Galerkin method for solving nonlinear ill-posed problems.Convergence results for the regularizing modified Levenberg-Marquardt scheme for the solution of nonlinear ill-posed problems have been proved.Based on these results,we propose a modified heuristic parameter choice rule to terminate the regularizing modified Levenberg-Marquardt scheme.By imposing certain conditions on the noise,we derive optimal convergence rates on the approximate solution under special source conditions.Numerical results are presented to illustrate the performance of the regularizing modified Levenberg-Marquardt scheme under the modified heuristic parameter choice.
