The horizontal diffusion coefficients of the operational model (T42L9) in numerical weather prediction are optimized by the steepest descent search of multi-dimensional optimization. In order to improve prediction acc...The horizontal diffusion coefficients of the operational model (T42L9) in numerical weather prediction are optimized by the steepest descent search of multi-dimensional optimization. In order to improve prediction accuracy in low latitudes, the optimum horizontal diffusion coefficients are chosen, with changing variation of the basic diffusion coefficient with the passage of time, and later forecasts are also made better. In view of the averages of forecast verifications of 9 cases, the forecasts with optimum diffusion coefficients are an improvement on operational forecasts. It means that the forecasts are got much better with optimum values of some important parameters by optimization in numerical weather prediction.展开更多
The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by ...The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize αk for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems.展开更多
There are many phenomena that generate polygonal tessellations on surfaces of 3D objects. One interesting example is the jackfruit, a multiple fruit found in the tropics. A recent study found the best-fit spherical Vo...There are many phenomena that generate polygonal tessellations on surfaces of 3D objects. One interesting example is the jackfruit, a multiple fruit found in the tropics. A recent study found the best-fit spherical Voronoi diagram from a photo of jackfruit skin, but the optimization was relative to the radius of the sphere and the height of the spikes. In this study, we propose a method for adjusting the position of the center of the sphere in addition to these parameters. Experiments were conducted using both ideal and real data. However, convergence with real data has not been confirmed due to relaxation of the convergence condition.展开更多
The steepest descent(or ascent)search is employed for finding optimum diffusion coefficients in T42L9G model,with a view to improving the model's computational stability or prediction accuracy.The method of the st...The steepest descent(or ascent)search is employed for finding optimum diffusion coefficients in T42L9G model,with a view to improving the model's computational stability or prediction accuracy.The method of the steepest descent search is first described,in which the golden section search is chosen as the fundamental one- dimensional search used in the multi-dimentional steepest descent search,and then the optimization of the dif- fusion coefficients is described.展开更多
文摘The horizontal diffusion coefficients of the operational model (T42L9) in numerical weather prediction are optimized by the steepest descent search of multi-dimensional optimization. In order to improve prediction accuracy in low latitudes, the optimum horizontal diffusion coefficients are chosen, with changing variation of the basic diffusion coefficient with the passage of time, and later forecasts are also made better. In view of the averages of forecast verifications of 9 cases, the forecasts with optimum diffusion coefficients are an improvement on operational forecasts. It means that the forecasts are got much better with optimum values of some important parameters by optimization in numerical weather prediction.
文摘The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize αk for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems.
基金Partly Supported by the Grant-in-Aid for Basic Research of MEXT(No.24360039)
文摘There are many phenomena that generate polygonal tessellations on surfaces of 3D objects. One interesting example is the jackfruit, a multiple fruit found in the tropics. A recent study found the best-fit spherical Voronoi diagram from a photo of jackfruit skin, but the optimization was relative to the radius of the sphere and the height of the spikes. In this study, we propose a method for adjusting the position of the center of the sphere in addition to these parameters. Experiments were conducted using both ideal and real data. However, convergence with real data has not been confirmed due to relaxation of the convergence condition.
文摘The steepest descent(or ascent)search is employed for finding optimum diffusion coefficients in T42L9G model,with a view to improving the model's computational stability or prediction accuracy.The method of the steepest descent search is first described,in which the golden section search is chosen as the fundamental one- dimensional search used in the multi-dimentional steepest descent search,and then the optimization of the dif- fusion coefficients is described.
