Stephen Cauley

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We present some superfast (O((m + n) log 2 (m + n)) complexity) and stable struc-tured direct solvers for m × n Toeplitz least squares problems. Based on the displacement equation, a Toeplitz matrix T is first transformed into a Cauchy-like matrix C, which can be shown to have small off-diagonal numerical ranks when the diagonal blocks are rectangular. We(More)
We introduce a technique that utilizes distributing computing resources for the efficient optimization of a traditional physical design problem. Specifically, we present a detailed placement strategy designed to exploit distributed computing environments, where the additional computing resources are employed in parallel to improve the optimization time. A(More)
We provide a new representation for the inverse of block tridiagonal and banded matrices. The new representation is shown to be numerically stable over a variety of block tridiagonal matrices, in addition of being more computationally efficient than the previously proposed techniques. We provide two algorithms for commonly encountered problems that(More)
We present an algorithm for the fast and accurate simulation of power/ground mesh structures. Our method is a direct (non-iterative) approach for simulation based upon a parallel matrix inversion algorithm. Through the use of additional computational resources, this distributed computing technique facilitates the simulation of large-scale power/ground(More)
The simulation of realistically sized devices under the Non-Equilibrium Greens Function (NEGF) formalism typically requires prohibitive amounts of memory and computation time. In order to meet the rising computational challenges associated with quantum-scale device simulation we offer a 2-D domain decomposition technique. This technique is applicable to a(More)
Through the Non-Equilibrium Green's Function (NEGF) formalism, quantum-scale device simulation can be performed with the inclusion of electron-phonon scattering. However, the simulation of realistically sized devices under the NEGF formalism typically requires prohibitive amounts of memory and computation time. Two of the most demanding computational(More)
This is to certify that the thesis/dissertation prepared By Entitled For the degree of Is approved by the final examining committee: Chair To the best of my knowledge and as understood by the student in the Research Integrity and Copyright Disclaimer (Graduate School Form 20), this thesis/dissertation adheres to the provisions of Purdue University's "(More)
We propose a fast structured selected inversion method for extracting the diagonal blocks of the inverse of a sparse symmetric matrix A, using the multifrontal method and rank structures. When A arises from the discretization of some PDEs and has a low-rank property (the intermediate dense matrices in the factorization have small off-diagonal numerical(More)
PURPOSE To improve slice coverage of gradient echo spin echo (GESE) sequences for dynamic susceptibility contrast (DSC) MRI using a simultaneous-multiple-slice (SMS) method. METHODS Data were acquired on 3 Tesla (T) MR scanners with a 32-channel head coil. To evaluate use of SMS for DSC, an SMS GESE sequence with two-fold slice coverage and same temporal(More)