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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)

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)

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 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)

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)

We present a technique for the fast and accurate simulation of large-scale VLSI interconnects with nonlinear devices, called SASIMI. The numerical efficiency of this technique is realized through linear-algebraic techniques that exploit the sparsity and structure of the matrices that are encountered in VLSI structures. Numerical results show that SASIMI is… (More)

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