Structured Matrices in Engineering and the Applied Sciences

Stephen Cauley
Massachusetts General Hospital

Room: UNIV 101

Apr 18, 2012 2:30 PM EDT

Structured matrices often arise in modeling, simulation, and optimizationof applications from engineering and the applied sciences. We consider two disparate emerging research applications where algorithms for semiseparable/ hierarchically semiseparable (HSS) matrices can ameliorate large-scale computational challenges.

First, semiseparable matrices are prevalent in the the simulation of quantum-scale devices. The Non-equilibrium Green's Function frameworkrequires efficient calculation and operations with a compact generatorrepresentation for the devices. We introduce distributed algorithms forsemiseparable matrices and demonstrate scalability on devices with over a million atomic-orbitals.

Next, the advent of sophisticated parallel sensing hardware in bio-medicalimaging has resulted in large-scale optimization problems. We will discussmodels for parallel/compressed sensing that can exploit HSS structures as a mathematical approximation tool for efficient optimization.