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

ABSTRACT:

The classical Multi-linear Algebra is branch and highlights how tensor-R operations work (over a commutative ring). It discusses associated algebra, external module algebra, symmetrical module algebra, coalgebra and hop algebras etc. However, more features of a higher-order tensor are required in modern multi-way data analysis and signal processing. Although the linear numerical algebra is an extension 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 new trends in further research. Our survey also includes an important part of a detailed bibliography. A new branch of computer math‟s is numerical multilinear algebra. It deals with the numerical handling by replacing matrix of higher-order tensors. Various computational issues related to the higher order tensors are included, such as decomposition of the tensor, tensor range calculation, own-value computation of the tensor, lower rank tensor approximations, numerical stability, and tensor calculation disturbance analysis, etc. This new business branch has a strong practical background and broad applications in the fields of digital image restore psychometrics, chemometrics, econometrics and multiway data analysis.