An Analysis of Numerical Practice Problems of Differential Equations of Multi-Linear Algebra

Exploring the Applications and Challenges of Numerical Multilinear Algebra in Modern Data Analysis

Abstract

The classical Multi-linear Algebra is branch and highlights how tensor-R operations work (overa commutative ring). It discusses associated algebra, external module algebra, symmetrical modulealgebra, coalgebra and hop algebras etc. However, more features of a higher-order tensor are required inmodern multi-way data analysis and signal processing. Although the linear numerical algebra is anextension of it, it has many essential differences and more difficulties than the linear numerical algebra.This paper presents an incomplete survey of state-of-the-art knowledge on this issue and shows newtrends in further research. Our survey also includes an important part of a detailed bibliography. A newbranch of computer math‟s is numerical multilinear algebra. It deals with the numerical handling byreplacing matrix of higher-order tensors. Various computational issues related to the higher ordertensors are included, such as decomposition of the tensor, tensor range calculation, own-valuecomputation of the tensor, lower rank tensor approximations, numerical stability, and tensor calculationdisturbance analysis, etc. This new business branch has a strong practical background and broadapplications in the fields of digital image restore psychometrics, chemometrics, econometrics and multiwaydata analysis.