Recently, several proposals for the generalization of Young's SOR method to the saddle point problem or the augmented system has been presented. One of the most practical versions is the SOR-like method given by Golub et al., [(2001). SOR-like methods for augmented systems. BIT, 41, 71-85.], where the convergence and the determination of its optimum parameters were given. In this article, a full characterization of the spectral radius of the SOR-like iteration matrix is given, and an explicit expression for the optimum parameter is given in each case. The new results also lead to different results to that of Golub et al. Besides, it is shown that by the choices of the preconditioning matrix, the optimum SOR-like iteration matrix has no complex eigenvalues, therefore, it can be accelerated by semi-iterative methods.
Small hydro-power generation shows strong uncertainty, which greatly affects the load forecasting work in small hydropower regions. Thus it's important to improve the accuracy of small hydropower generation load forecasting. At present, the most commonly used forecasting method is artificial neural network, which has strong adaptability and learning ability but poor generalization and easily falls into local minimum. The random fluctuation of small hydropower is not taken into consideration. This paper was based on analyzing the characteristics of small hydropower generation load, combining the wavelet transform to decompose the historical load to establish the prediction model for each component feature. Particle Swarm Optimization (Algorithm) was used to optimize initial weights and thresholds of neural networks before the prediction. After verified by real case in a rich small hydropower area in some province, the load prediction precision reaches 93.7%, higher than the precision of the high-voltage system criteria for assessing. The accuracy and effectiveness of the method is verified.
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