Stephen Cauley

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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 propose a structured selected inversion method for extracting the diagonal (and certain o↵-diagonal) blocks of the inverse of a sparse symmetric matrix A, using the multifrontal method and rank structures. A structured multifrontal LDL factorization is computed for A with a forward traversal of the assembly tree, which yields a sequence of data-sparse(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)
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)
Some structured multifrontal methods for nonsymmetric sparse matrices are developed, which are applicable to discretized PDEs such as Helmholtz equations on finite di↵erence or irregular meshes. Unlike various existing structured direct solvers, which often focus on symmetric positive definite or symmetric matrices, our methods consider the issues for(More)
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