State space orderings for Gauss-Seidel in Markov chains revisited
- Bilkent Univ., Ankara (Turkey)
Symmetric state space orderings of a Markov chain may be used to reduce the magnitude of the subdominant eigenvalue of the (Gauss-Seidel) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the dominant term of the Gauss-Seidel splitting (that is, the term approximating the coefficient matrix) do not necessarily converge faster. An ordering of a Markov chain that satisfies Property-R is semi-convergent. On the other hand, there are semi-convergent symmetric state space orderings that do not satisfy Property-R. For a given ordering, a simple approach for checking Property-R is shown. An algorithm that orders the states of a Markov chain so as to increase the likelihood of satisfying Property-R is presented. The computational complexity of the ordering algorithm is less than that of a single Gauss-Seidel iteration (for sparse matrices). In doing all this, the aim is to gain an insight for faster converging orderings. Results from a variety of applications improve the confidence in the algorithm.
- Research Organization:
- Front Range Scientific Computations, Inc., Lakewood, CO (United States)
- OSTI ID:
- 440705
- Report Number(s):
- CONF-9604167--Vol.2; ON: DE96015307
- Country of Publication:
- United States
- Language:
- English
Similar Records
Accuracy increase in waveform Gauss Seidel
A parallel Gauss-Seidel algorithm for sparse power system matrices