We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially stochastically with respect to expectation values only. Compared to a fully stochasti...

Definition 4. BBP is the class of languages L that have a poly time algorithm A that for any string x, and a long random string r, • x ∈ L⇒ Pr[A(x, r)rejects] ≤ 1/100 • x 6∈ L⇒ Pr[A(x, r)accepts] ≤ 1/100 Observation 5. By repeating this algorithm k times with random strings r1...rk, the probability that the majority of the outcomes is incorrect is 1/2Ω(k) (proved this with Chernoff bound on a p...

The details of doing a Monte Carlo direct lighting calculation are presented. For direct lighting from multiple luminaires, a method of sending one shadow ray per viewing ray is presented, and it is argued that this is preferable for scenes with many luminaires. Some issues of the design of probability densities on unions of luminaire surfaces are discussed.

Quantum Monte Carlo is an important and complementary alternative to density functional theory when performing computational electronic structure calculations in which high accuracy is required. The method has many attractive features for probing the electronic structure of real atoms, molecules and solids. In particular, it is a genuine many-body theory with a natural and explicit description ...

We discuss a sampling algorithm which generates flat histogram in energy. In combination with transition matrix Monte Carlo, the density of states and derived quantities such as entropy and free energy as a function of temperature can be computed in a single simulation.