Fast Monte Carlo Algorithms for Matri es II: Computing a Low-Rank Approximation to a Matrix

Fast Monte Carlo Algorithms for Matri es III: Computing a Compressed Approximate Matrix De omposition

Evaluating Performance of Algorithms in Lung IMRT: A Comparison of Monte Carlo, Pencil Beam, Superposition, Fast Superposition and Convolution Algorithms

Background: Inclusion of inhomogeneity corrections in intensity modulated small fields always makes conformal irradiation of lung tumor very complicated in accurate dose delivery.Objective: In the present study, the performance of five algorithms via Monte Carlo, Pencil Beam, Convolution, Fast Superposition and Superposition were evaluated in lung cancer Intensity Modulated Radiotherapy plannin...

Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix

In many applications, the data consist of (or may be naturally formulated as) an m×n matrix A. It is often of interest to find a low-rank approximation to A, i.e., an approximation D to the matrix A of rank not greater than a specified rank k, where k is much smaller than m and n. Methods such as the singular value decomposition (SVD) may be used to find an approximation to A which is the best ...

Computational aspects of lattice rule construction for numerical integration

Popular methods for approximating high-dimensional integrals over [0, 1)s are the so called quasi-Monte Carlo methods, taking the mean of n quasirandom points as an approximation for the integral under consideration. An easy and theoretically convenient family of quasi-Monte Carlo methods are rank-1 lattice rules. For these, component-by-component algorithms exist which, e.g. for a Korobov spac...

Sampling and multilevel coarsening algorithms for fast matrix approximations

This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques, possibly combined with random sampling. A multilevel coarsening technique is proposed which utilizes a hypergraph associated with the data matrix and a graph coa...