Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices

It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general $H-$matrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper

The Relationship Between Teachers’ Perception Towards School Climate and Their Decision-Making Styles at a Primary School in Anning District, Lanzhou City, China

 The main purpose of this study was to determine the relationship between teachers’ perception towards school climate and their decisionmaking styles at a selected primary school in Anning District, Lanzhou city, China. The study firstly assessed the teachers’ perception towards school climate, examined the teachers’ decision-making styles; lastly tested the relationship between these two main variables. A total of 71 full-time teachers replied the questionnaires adopted by the researcher. Means and Standard Deviations were used to report the teachers’ perception towards school climate and their decision-making styles; Pearson Product Moment Correlation Coefficient analysis was applied to test the relationship between these two variables. The results showed that, the teachers in the target school had a relatively positive attitude towards school climate. Besides, teachers’ most preferred decision-making style was group decision-making style. The Pearson Correlation test indicated that there was a significant relationship between teachers’ perception towards school climate and their decisionmaking styles at the selected primary school in Anning District, Lanzhou city, China.