An iterative algorithm for solving ill-conditioned linear least squares problems

Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.

Analysis of the negative effects of groundwater exploitation on geological environment in Asia

This paper summarizes the negative effects on geological environment caused by groundwater exploitation and its distribution. There are seven main types of the geological environment negative effects, which are generally as follows:(1) Constant decrease of groundwater level is mainly distributed in China(East Asia), India(South Asia), Tajikistan(Central Asia) and Saudi Arabia(West Asia);(2) land subsidence occurs mainly in eastern plains of East Asia and west Siberian Plain of North Asia;(3) seawater intrusion occurs mainly in China, Japan and South Korea in East Asia, Philippines and Indonesia in Southeast Asia, the Indian coastal areas in South Asia;(4) groundwater level decline caused by groundwater exploitation in oil fields;(5) mining collapse is mainly in 50° to 70° north latitude band;(6) the total area of karst collapse in China of East Asia is as much as 197.05 km^2; and(7) ground fracture is mainly distributed in the North China Plain, Fenwei Plain and the Yangtze River Delta. Asia can be divided into 6 zones in terms of the geological environment negative effect caused by groundwater exploitation. According to analysis, with the increasing intensity of human activities, geological environment issues become more and more serious, therefore it is vital to control the human activities within the scope of 5× 10~5 people/km^2 to 9.9× 10~5 people/km^2 for the effective control of the size of the affected area by geological environment problems.

Baduanjin exercise improved premenstrual syndrome symptoms in Macao women

OBJECTIVE: To investigate the effect of Baduanjin,a traditional Chinese medical exercise, on improving premenstrual syndrome(PMS) symptoms in women.METHODS: Forty reproductive age women with PMS in Macao practiced standardized Baduanjin exercise for three menstrual cycles. A questionnaire,the daily record of severity of problems(DRSP), was used to measure symptom severity. DRSP was filled out every days tarting from the last cycle before exercise(i.e., the first menstrual cycle) to the third cycle after exercise initiation(i.e., the fourth menstrual cycle). The total scores and the scores of each item during the 5 premenstrual days and follicular phase(5-9 postmenstrual days)were calculated.RESULTS: After exercise, the total DRSP scores dur-ing the 5 premenstrual days and differences in the total DRSP scores between the 5 premenstrual days and the follicular phase were both significantly reduced. Of note, the physical symptom total scores in the 5 premenstrual days and the differences between its total score in the 5 premenstrual days and in the follicular phase were both significantly reduced. The differences between the total scores of depressed mood, anxious mood, loss of interest,and reduction in social activity during the 5 premenstrual days and the follicular phase were also reduced.CONCLUSION: Baduanjin exercise was able to improve the mental and especially the physical symptoms of PMS.