Numerical Results for the Metropolis Algorithm

Abstract

This paper deals with the spectrum of an operator associated with a special kind of random walk. The operator is related to the Metropolis algorithm, an important tool of large-scale scientific computing. The spectrum of this operator has both dis-I crete and continuous parts. There is an interesting challenge due to the fact that any finite-dimensional approxirnation has only eigenval ues. Patterns are presented which give an idea of the full spectrum of this operator.

Keywords:

• Metropolis algorithm
• random walk
• continuous spectrum