Circulant preconditioners for failure prone manufacturing systems
A failure prone one-machine manufacturing system is considered. The machine-inventory process is modeled as an irreducible continuous-time Markov chain. At first, the generator matrix for the machine-inventory system is derived. A preconditioner is constructed by taking a circulant approximation of the near-Toeplitz structure of the generator matrix. It is proved that the preconditioned matrix has singular values clustered around one. Numerical examples show that the corresponding preconditioned conjugate gradient method converges very fast.
preconditioned conjugate gradient method
scientific article; zbMATH DE number 1083216
scientific article