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.

A Hybrid Monte Carlo method (HMC) method is proposed in this article for estimating the system reliability of a stochastic network without needing to know all of the minimal pathsets/cutsets (MPs/MCs) in advance. The analysis indicates that the proposed method is efficient when compared to the crude Monte Carlo method (CMC).

We study optimal stochastic (or Monte Carlo) quadrature formulas for convex functions. While nonadaptive Monte Carlo methods are not better than deterministic methods we prove that adaptive Monte Carlo methods are much better. Abstract. We study optimal stochastic (or Monte Carlo) quadrature formulas for convex functions. While nonadaptive Monte Carlo methods are not better than deter-ministic ...

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This paper describes a method for the Monte Carlo simulation of two correlated random variables. The author analyses linear combinations of stochastically independent random variables that are equally distributed over the interval (0; 1) (\random numbers") and also examines their distribution. If a suitable matrix of coeecients is chosen, the subsequent transformation results in random variable...