关键词： 数学算法   计算机编程方式   优化手段  

摘要： 我国经济与科技迅猛发展,以计算机行业为代表,计算机编程方式正在不断地创新与优化。针对计算机编程方式的优化改良,已经成为信息技术行业中的热点问题,也受到了社会各界的广泛关注。本文将从数学算法应用开始,针对其对计算机编程优化的基本作用,展开细致的分析与讨论。

关键词： 分式方程   数学运算   深度学习  

摘要： 课堂教学中经常有学生不按运算法则所强调的"规范解法"解分式方程,这也是数学运算中常见的现象.数学运算法则课深度学习的价值在于让学生经历法则的提炼过程,感受法则程序性解决问题的思维价值,从而发展学生数学运算的核心素养.数学运算深度学习的着力点是在深切体验中透析算理,在深刻理解中提炼算法,在深入思维中优化策略.

关键词： 数学算法   计算机编程   优化   分析研究  

摘要： 随着现代化信息技术的进步,社会发展不断加快,使得社会的关注点从工业转移到计算机领域的发展。计算机行业在现代社会中处于重要的发展趋势,在社会的发展过程中任何方面都离不开计算机信息技术,当前计算机的软件的主要语言方式就是利用编程完成,计算机编程的效果影响着软件工作效率。而数学算法是数学学科的一种特殊内容,可以对问题进行总结归纳并得以有效解决。计算机技术中合理利用数学算法对计算机编程的优化和改进,这样有利于计算机技术在今后的创新发展。

关键词： 图像处理   边缘检测   Canny算子   数学形态学   滤波  

摘要： 为了更好地提取图像的边缘信息并且抑制噪声,本文设计了一种基于数学形态学预处理的Canny算子边缘检测算法.通过将该算法与一般边缘检测算法以及Canny算法的仿真结果进行比较,可以发现该算法在边缘检测及消除噪声方面较之其他算法可取得更优的性能.

关键词： 高中数学   算法思想   导入  

摘要： 本文主要以高中数学教学中算法思想的导入分析为重点进行阐述,为提高高中生数学学习能力与综合素养做铺垫。

关键词： PARAFAC2   direct fitting algorithm  

摘要： The PARAFAC2 decomposition has attracted growing research interest. To compute it, the direct fitting (DF) algorithm is usually employed. In this contribution, we propose to incorporate semi-algebraic approaches for the computation of PARAFAC in the DF algorithm and explore how it should be adapted to largely exploit the resulting diversity in the estimates of factor matrices to enhance the robustness and efficiency. Three versions have been tailored and recommended for different parameter settings according to, e.g., the number of components or tensor dimensions. Extensive numerical simulations have been conducted with both synthetic and measured biomedical as well as wine data to validate the improved performance of the proposed DF algorithms. In addition, it has been shown that applying the geometric search on top of the proposed DF algorithms further boosts their performance.

关键词： Tensor   Canonical polyadic decomposition   Double coupled   Algebraic algorithm   Uniqueness  

摘要： Double coupled canonical polyadic decomposition (DC-CPD) decomposes multiple tensors with coupling in the first two modes, into minimal number of rank-1 tensors that also admit the double coupling structure. It has a particular interest in joint blind source separation (J-BSS) applications. In a preceding paper, we proposed an algebraic algorithm for underdetermined DC-CPD, of which the factor matrices in the first two modes of each tensor may have more columns than rows. It uses a pairwise coupled rank-1 detection mapping to transform a possibly underdetermined DC-CPD into an overdetermined DC-CPD, which can be solved algebraically via generalized eigenvalue decomposition (GEVD). In this paper, we generalize the pairwise or second-order coupled rank-1 detection mapping to an arbitrary order K >= 2. Based on this generalized coupled rank-1 detection mapping, we propose a broad framework for the algebraic computation of DC-CPD, which consists of a series of algorithms with more relaxed working assumptions, each corresponding to a fixed order K >= 2. Deterministic and generic uniqueness conditions are provided. We will show through analysis and numerical results that our new uniqueness conditions for DC-CPD are more relaxed than the existing results for DC-CPD and CPD. We will further show, through simulation results, the performance of the proposed algebraic DC-CPD framework in approximate DC-CPD and a J-BSS application, in comparison with existing DC-CPD and CPD algorithms.