Abstract
This paper is concerned with solving some structured multi-linear systems, especially focusing on the equations whose coefficient tensors are M-tensors, or called M-equations for short. We prove that a nonsingular M-equation with a positive right-hand side always has a unique positive solution. Several iterative algorithms are proposed for solving multi-linear nonsingular M-equations, generalizing the classical iterative methods and the Newton method for linear systems. Furthermore, we apply the M-equations to some nonlinear differential equations and the inverse iteration for spectral radii of nonnegative tensors.
| Original language | English |
|---|---|
| Pages (from-to) | 689-715 |
| Number of pages | 27 |
| Journal | Journal of Scientific Computing |
| Volume | 68 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Aug 2016 |
Scopus Subject Areas
- Software
- Theoretical Computer Science
- Numerical Analysis
- General Engineering
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Gauss–Seidel method
- Inverse iteration
- Jacobi method
- M-tensor
- Multi-linear system
- Newton method
- Nonnegative solution
- Nonnegative tensor
- Triangular system