A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020
A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020
复制标题
1995-2020 年四元数和几何代数在工程和计算机科学中的应用综述
DOI：
10.1109/access.2021.3097756
复制
发表时间：
2021
期刊：
影响因子：
3.9
通讯作者：
E. Bayro
中科院分区：
文献类型：
--
作者：
E. Bayro
几何代数（GA）已被证明是数学，物理，计算机科学和工程的高级语言。本文综述了从1995年到2020年四元数代数和遗传算法在计算机科学与工程中的应用。在简单介绍遗传算法的基础上，综述了遗传算法在各个领域的应用.讨论了遗传算法在计算机科学与工程中应用的特点。此外，分析了许多研究者提出的各种应用的挑战和前景。我们分析了使用遗传算法在图像处理，计算机视觉，神经计算，量子计算，机器人建模，控制和跟踪，以及计算机硬件性能的改进的发展。我们相信，到目前为止，GA已被证明是一个强大的几何语言的各种应用。此外，有证据表明，这是适当的几何语言，以解决各种现有的问题，因此，一步一步的GA为基础的算法应继续进一步发展。我们还相信，这一广泛的审查将指导和鼓励研究人员继续推进智能机器的几何计算。
Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics, computer science, and engineering. This review presents a comprehensive study of works on Quaternion Algebra and GA applications in computer science and engineering from 1995 to 2020. After a brief introduction of GA, the applications of GA are reviewed across many fields. We discuss the characteristics of the applications of GA to various problems of computer science and engineering. In addition, the challenges and prospects of various applications proposed by many researchers are analyzed. We analyze the developments using GA in image processing, computer vision, neurocomputing, quantum computing, robot modeling, control, and tracking, as well as improvement of computer hardware performance. We believe that up to now GA has proven to be a powerful geometric language for a variety of applications. Furthermore, there is evidence that this is the appropriate geometric language to tackle a variety of existing problems and that consequently, step-by-step GA-based algorithms should continue to be further developed. We also believe that this extensive review will guide and encourage researchers to continue the advancement of geometric computing for intelligent machines.