Multiple decompositions for computational convenience

Computational optimization for tensor decompositions

Further advances depend critically on algorithms that are robust, accurate, numerically stable, and fast. Despite widespread interest, the computational tools available to practitioners have not changed dramatically for nearly four decades. State-of-the-art methods are based on simple alternating least squares (ALS); this approach is often slow to converge and there are few guarantees that it w...

Array Decompositions for Nonuniform Computational Environments

Two-dimensional arrays are useful in a large variety of scienti c and engineering applications. Parallelization of these applications requires the decomposition of array elements among di erent machines. Several data-decomposition techniques have been studied in the literature for machines with uniform computational power. In this paper we develop new methods for decomposing arrays into a clust...

Physical and Computational Domain Decompositions for Modeling Subsurface Flows

Modeling of multiphase flow in permeable media plays a central role in subsurface environmental remediation as well as in problems associated with production of hydrocarbon energy from existing oil and gas fields. Numerical simulation is essential for risk assessment, cost reduction, and rational and efficient use of resources. The contamination of groundwater is one of the most serious environ...

Double Coset Decompositions and Computational Harmonic Analysis on Groups

In this paper we introduce new techniques for the eecient computation of a Fourier transform on a nite group. We use the decomposition of a group into double cosets and a graph theoretic indexing scheme to derive algorithms that generalize the Cooley-Tukey FFT to arbitrary nite groups. We apply our general results to special linear groups and low rank symmetric groups, and obtain new eecient al...

Convenience Sampling