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In applications ranging from DNA sequencing through archeological dating to sparse matrix reordering, a recurrent problem is the sequencing of elements in such a way that highly correlated pairs of elements are near each other. That is, given a correlation function f reflecting the desire for each pair of elements to be near each other, find all… (More)

We present support theory, a set of techniques for bounding extreme eigenvalues and condition numbers for matrix pencils. Our intended application of support theory is to enable proving condition number bounds for preconditioners for symmetric, positive definite systems. One key feature sets our approach apart from most other works: We use support numbers… (More)

1. Introduction. Partitioning and load-balancing are important issues in parallel scientific computing. The goal is to distribute data (and work) evenly among processors such as to reduce communication cost and achieve maximal performance. Graph partitioning has long served as a useful model for load balancing in parallel computing. Data are represented as… (More)

We show in this note how support preconditioners can be applied to a class of linear systems arising from use of the finite element method to solve linear elliptic problems. Our technique reduces the problem, which is symmetric and positive definite, to a symmetric positive definite diagonally dominant problem. Significant theory has already been developed… (More)

In parallel adaptive applications, the computational structure of the applications changes over time, leading to load imbalances even though the initial load distributions were balanced. To restore balance and to keep communication volume low in further iterations of the applications, dynamic load balancing (repartitioning) of the changed computational… (More)

This paper analyzes a novel method for constructing preconditioners for diagonally-dominant symmetric positive-definite matrices. The method discussed here is based on a simple idea: we construct M by simply dropping offdiagonal nonzeros from A and modifying the diagonal elements to maintain a certain row-sum property. The preconditioners are extensions of… (More)

Using a longitudinal study design, two strains of Alzheimer's disease (AD) model mice, one expressing β-amyloid plaques and one expressing Tau protein-associated neurofibrillary tangles were assessed for olfactory and visuospatial learning and memory and their performance compared to that of age-matched controls. No significant difference between AD and… (More)

- Ariful Azad, Mahantesh Halappanavar, Siva Rajamanickam, Erik G. Boman, Arif Khan, Alex Pothen
- 2011

—We design, implement, and evaluate algorithms for computing a matching of maximum cardinality in a bipartite graph on multi-core and massively multithreaded computers. As computers with larger number of slower cores dominate the commodity processor market, the design of multithreaded algorithms to solve large matching problems becomes a necessity. Recent… (More)

- Karen D. Devine, Erik G. Boman, Robert T. Heaphy, Bruce A. Hendrickson, James D. Teresco, Jamal Faik +2 others
- 2004

Data partitioning and load balancing are important components of parallel computations. Many different partitioning strategies have been developed, with great effectiveness in parallel applications. But the load-balancing problem is not yet solved completely; new applications and architectures require new partitioning features. Existing algorithms must be… (More)