|
延拓式教学在数值并行计算课程中的应用研究
|
Abstract:
延拓式教学是一种内容更加灵活多样的教学模式,对培养学生的实践能力和创新能力具有重要意义。文章将从实施方式、效果评价和影响因素等方面,以数值并行计算课程中的卡茨马兹方法为例,对其延拓式教学进行研究,旨在帮助学生更加深刻地理解卡茨马兹算法及其变种之间的联系,以便建立牢固的知识框架。
Extension teaching is a more flexible and diverse instructional approach that holds significant importance in cultivating students’ practical and innovative capabilities. This paper explores extension teaching in the context of a Numerical Parallel Computing course, using the Kaczmarz method as a case study. It focuses on implementation methods, effectiveness evaluation, and influencing factors. The aim is to deepen students’ understanding of the connections between the Kaczmarz algorithm and its variants, thereby establishing a solid knowledge framework.
[1] | 刘子心, 刘章军, 孙治国. 弹性力学探究式案例教学的设计与实践[J]. 高等建筑教育, 2022, 31(5): 108-117. |
[2] | 朱小扣, 朱嘉懿. 例谈不等式解题中的多元性和延拓性[J]. 数理化解题研究, 2017(16): 35-36. |
[3] | 杨湘豫. “均值”的延拓式教学设计[J]. 湖南理工学院学报(自然科学版), 2016, 29(1): 79-82. |
[4] | 李晓梅, 吴建平. 数值并行算法[M]. 北京: 科学出版社, 2014. |
[5] | Kaczmarz, S. (1937) Angenaherte auflosung von systemen linearer gleichungen. Bulletin International de l’Academie Polonaise des Sciences A, 35, 355-357. |
[6] | Strohmer, T. and Vershynin, R. (2008) A Randomized Kaczmarz Algorithm with Exponential Convergence. Journal of Fourier Analysis and Applications, 15, 262-278. https://doi.org/10.1007/s00041-008-9030-4 |
[7] | Bai, Z. and Wu, W. (2018) On Greedy Randomized Kaczmarz Method for Solving Large Sparse Linear Systems. SIAM Journal on Scientific Computing, 40, A592-A606. https://doi.org/10.1137/17m1137747 |
[8] | Necoara, I. (2019) Faster Randomized Block Kaczmarz Algorithms. SIAM Journal on Matrix Analysis and Applications, 40, 1425-1452. https://doi.org/10.1137/19m1251643 |