Abstract
A natural generalization of the Jacobi and Gauss-Seidel iterations for interval systems is to allow the matrices to reside in convex polytopes. In order to apply the standard convergence criteria involving M-matrices to iterations for polytopic systems, we derive conditions for a convex polytope of matrices to be a polytope of M-matrices in terms of its vertices. We show how the conditions are used in the convergence analysis of iterations for block and nonlinear polytopic systems.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 123-137 |
| Number of pages | 15 |
| Journal | Reliable Computing |
| Volume | 6 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2000 |
| Externally published | Yes |
ASJC Scopus subject areas
- Software
- Computational Mathematics
- Applied Mathematics