Note on the equations of diffusion operators associated to a positive matrix
Provides a theoretical decomposition of matrix-vector products for convergence analysis, but is incremental and domain-specific.
The paper develops a general framework for diffusion operators from a positive matrix, showing how it can prove and improve convergence of a fixed-point problem in matrix iteration schemes.
In this paper, we describe the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We show how this can be applied to prove and improve the convergence of a fixed point problem associated to the matrix iteration scheme. The approach can be understood as a decomposition of the matrix-vector product operation in elementary operation at the vector entry level.