Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the co...Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the coefficient matrix A.The results obtained by this approach for matrices with no structure and with indefinite symmetric part were encouraging when compare with other recent and well-known techniques.In this work,we proposed to extend the OPALS approach for solving the Linear Least-Squares Problem(LLSP)and the Minimum Norm Linear System Problem(MNLSP)using any iterative low-cost gradient-type method,avoiding the construction of the matrices AT A or AAT,and taking full advantage of the structure and form of the gradient of the proposed nonlinear objective function in the gradient direction.The combination of those conditions together with the choice of the initial iterate allow us to produce a novel and efficient low-cost numerical scheme for solving both problems.Moreover,the scheme presented in this work can also be used and extended for the weighted minimum norm linear systems and minimum norm linear least-squares problems.We include encouraging numerical results to illustrate the practical behavior of the proposed schemes.展开更多
The Taylor dispersion method was used to measure diffusion coefficients of three-component liquid systems. An improved constrained nonlinear least-square method was used to evaluate the ternary diffusion coefficients ...The Taylor dispersion method was used to measure diffusion coefficients of three-component liquid systems. An improved constrained nonlinear least-square method was used to evaluate the ternary diffusion coefficients directly by fitting the mathematical solutions of the dispersion equation to eluted solute peaks detected using a differential refractometer. Diffusion coefficients of the three-component system of acetone-benzene-CCl4, determined at 25℃, were used to test the procedure. The measured diffusion coefficients were compared with values obtained by optical interferometry and the diaphragm cell method. Ternary diffusion coefficients are also determinated for solutions of 1-hexanol-hexane-toluene and 1-propanol- water-ethylene glycol at 25℃, with an accuracy of approximately 0.05 m^2·s^- 1.展开更多
This paper studies a problem of optimal investment and consumption with early retirement option under constant elasticity variation(CEV)model with finite horizon.Two risky assets are involved in the model with one fol...This paper studies a problem of optimal investment and consumption with early retirement option under constant elasticity variation(CEV)model with finite horizon.Two risky assets are involved in the model with one following geometric Brownian motion and the other a CEV model.This problem is a kind of two dimensional mixed control and optimal stopping problems with finite horizon.The existence and continuity of the optimal retirement threshold surfaces are proved and the working and retirement regions are characterized theoretically.Least-squares Monte-Carlo methods are developed to solve this mixed control and optimal stopping problem.The algorithms are well implemented and the optimal retirement threshold surfaces,optimal investment strategies and the optimal consumptions are drawn via examples.展开更多
A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for ...A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for each single peak contains a step function, a Gaussian function and an exponential tail function. Parameters in the model are obtained by weighted nonlinear least-squares fitting method. In the application, six kinds of elements＇ characteristic X-ray spectra are obtained by Si （PIN） detector, and fitted out by the established DRF model. Reduced chi-square values are at the interval of 1.11-1.25. Other applications of the method are also discussed.展开更多
文摘Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the coefficient matrix A.The results obtained by this approach for matrices with no structure and with indefinite symmetric part were encouraging when compare with other recent and well-known techniques.In this work,we proposed to extend the OPALS approach for solving the Linear Least-Squares Problem(LLSP)and the Minimum Norm Linear System Problem(MNLSP)using any iterative low-cost gradient-type method,avoiding the construction of the matrices AT A or AAT,and taking full advantage of the structure and form of the gradient of the proposed nonlinear objective function in the gradient direction.The combination of those conditions together with the choice of the initial iterate allow us to produce a novel and efficient low-cost numerical scheme for solving both problems.Moreover,the scheme presented in this work can also be used and extended for the weighted minimum norm linear systems and minimum norm linear least-squares problems.We include encouraging numerical results to illustrate the practical behavior of the proposed schemes.
基金Supported by the National Natural Science Foundation of China (No. 29836130) and the German Research Foundation of Germany
文摘The Taylor dispersion method was used to measure diffusion coefficients of three-component liquid systems. An improved constrained nonlinear least-square method was used to evaluate the ternary diffusion coefficients directly by fitting the mathematical solutions of the dispersion equation to eluted solute peaks detected using a differential refractometer. Diffusion coefficients of the three-component system of acetone-benzene-CCl4, determined at 25℃, were used to test the procedure. The measured diffusion coefficients were compared with values obtained by optical interferometry and the diaphragm cell method. Ternary diffusion coefficients are also determinated for solutions of 1-hexanol-hexane-toluene and 1-propanol- water-ethylene glycol at 25℃, with an accuracy of approximately 0.05 m^2·s^- 1.
基金supported by the National Natural Science Foundation of China(Grant No.12071373)by the Fundamental Research Funds for the Central Universities of China(Grant No.JBK1805001)+1 种基金The work of J.Xing was supported by the National Natural Science Foundation of China(Grant No.12101151)by the Guizhou Key Laboratory of Big Data Statistical Analysis(Grant No.[2019]5103).
文摘This paper studies a problem of optimal investment and consumption with early retirement option under constant elasticity variation(CEV)model with finite horizon.Two risky assets are involved in the model with one following geometric Brownian motion and the other a CEV model.This problem is a kind of two dimensional mixed control and optimal stopping problems with finite horizon.The existence and continuity of the optimal retirement threshold surfaces are proved and the working and retirement regions are characterized theoretically.Least-squares Monte-Carlo methods are developed to solve this mixed control and optimal stopping problem.The algorithms are well implemented and the optimal retirement threshold surfaces,optimal investment strategies and the optimal consumptions are drawn via examples.
基金Supported by National Natural Science Foundation of China(40974065, 41025015)Scientific and Technological Innovative Team in Sichuan Province(2011JTD0013)"863" Program of China(2012AA063501)
文摘A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for each single peak contains a step function, a Gaussian function and an exponential tail function. Parameters in the model are obtained by weighted nonlinear least-squares fitting method. In the application, six kinds of elements＇ characteristic X-ray spectra are obtained by Si （PIN） detector, and fitted out by the established DRF model. Reduced chi-square values are at the interval of 1.11-1.25. Other applications of the method are also discussed.
