论文标题
数学的八个时代有关过去和将来的矩阵计算
The Eight Epochs of Math as regards past and future Matrix Computation
论文作者
论文摘要
本文对时代进行了个人评估，从古代和明天的矩阵计算中取得了进步。 我们追踪数字系统和基本代数的开发，以及从公元前2000年左右到当前实时神经网络计算的高斯消除方法的使用以求解时间变化的线性方程。 我们包括在公元3世纪的中国以及9世纪的印度和波斯的相关进展，并讨论了14至17世纪公元14至17世纪中欧和日本的矢量和矩阵的概念起源。 其次是针对矩阵特征值的多项式根发现器研究150年的CUL-DE-SAC，以及上世纪的出色有用的矩阵迭代方法和Francis的特征值算法。 然后，我们解释了最初使用的初始值问题解决器通过神经网络来掌握时变线性和非线性矩阵方程。 最后，我们以多级处理器的新硬件方案的简短展望，这些处理器超出了我们所有过去和当前的电子计算机都使用的0-1 Base 2框架。
This paper gives a personal assessment of Epoch making advances in Matrix Computations from antiquity and with an eye towards tomorrow. We trace the development of number systems and elementary algebra, and the uses of Gaussian Elimination methods from around 2000 BC on to current real-time Neural Network computations to solve time-varying linear equations. We include relevant advances from China from the 3rd century AD on, and from India and Persia in the 9th century and discuss the conceptual genesis of vectors and matrices in central Europe and Japan in the 14th through 17th centuries AD. Followed by the 150 year cul-de-sac of polynomial root finder research for matrix eigenvalues, as well as the superbly useful matrix iterative methods and Francis' eigenvalue Algorithm from last century. Then we explain the recent use of initial value problem solvers to master time-varying linear and nonlinear matrix equations via Neural Networks. We end with a short outlook upon new hardware schemes with multilevel processors that go beyond the 0-1 base 2 framework which all of our past and current electronic computers have been using.
