A new method for the estimate of global optimum value is proposed. The method has a descent character with respect to the objective function value. Preliminary numerical experiments for the method are also presented.
An approach for generating test problems by a computer using the Monte Carlo method based upon user-given characterizations is described.A single point X~* is prespocified by the user to be a solution of the test prob...An approach for generating test problems by a computer using the Monte Carlo method based upon user-given characterizations is described.A single point X~* is prespocified by the user to be a solution of the test problems.The approach is flex- ible enough to specify function values,gradients,Hesse,degeneracy degree and ill- conditioned degree at the point X~*.Other numerical features such as indefiniteness, convexity are also under user's control.展开更多
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
We discuss semiconvergence of the extrapolated iterative methods for solving singular linear systems. We obtain the upper bounds and the optimum convergence factor of the extrapolation method as well as its associated...We discuss semiconvergence of the extrapolated iterative methods for solving singular linear systems. We obtain the upper bounds and the optimum convergence factor of the extrapolation method as well as its associated optimum extrapolation parameter. Numerical examples are given to illustrate the theoretical results.展开更多
文摘A new method for the estimate of global optimum value is proposed. The method has a descent character with respect to the objective function value. Preliminary numerical experiments for the method are also presented.
文摘An approach for generating test problems by a computer using the Monte Carlo method based upon user-given characterizations is described.A single point X~* is prespocified by the user to be a solution of the test problems.The approach is flex- ible enough to specify function values,gradients,Hesse,degeneracy degree and ill- conditioned degree at the point X~*.Other numerical features such as indefiniteness, convexity are also under user's control.
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.
基金supported by the National Natural Science Foundation of China under grant 10371056the Foundation for the Authors of the National Excellent Doctoral Thesis Award of China under grant 200720+1 种基金the Natural Science Foundation of Jiangsu Province under grant BK2006725the College Natural Science Foundation of Jiangsu Province under grant 05KJB110062
文摘We discuss semiconvergence of the extrapolated iterative methods for solving singular linear systems. We obtain the upper bounds and the optimum convergence factor of the extrapolation method as well as its associated optimum extrapolation parameter. Numerical examples are given to illustrate the theoretical results.
