I work in the field of numerical linear algebra, primarily with Krylov subspace projection methods. My primary focus right now is on applications of Krylov subspace recycling. I also work on algorithms for solving structured linear systems such as nearly Hermitian systems and families systems which differ by multiples of the identity. I enjoy work in the entire spectrum, from mathematical theory and algorithm design to the more practical implementation of an algorithm for high performance computing. I also work on data analysis projects and have an interest in data mining.
I have listed all papers, presentations, and projects on which I have worked. I also list all workshops I have attended. If possible, I will include links to relevant websites and to any papers for which a copy exists on the internet.
For more information, please see my CV, Research Statement and Teaching Statement.
Publications
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Automatic Detection of Weather Fronts
We propose a new algorithm for the detection of weather fronts from discrete weather data generated by weather forecasting software. Given data for a snapshop in time, the algorithm detects cold and warm fronts and draws them on a weather map. Given multiple time frames, the algorithm creates a smooth animation of the weather fronts as they travel. Detection of occluded fronts (formed when a fast-moving cold front overtakes a warm front) is also treated.
In Preparation
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Krylov Subspace Recycling for Sequences of Shifted Linear Systems
We extend the GCRODR algorithm (GMRES with recycling) of Parks et al [SIAM J. Sci. Comput. 2006] to solve sequences of nearby linear systems where for each matrix in the sequence, we solve multiple systems differing by a multiple of the identity. We present numerical examples involving systems arising in lattice quantum chromodynamics.
In Preparation
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Block Krylov Subspace Recycling
We extend the GCRODR algorithm (GMRES with recycling) of Parks et al [SIAM J. Sci. Comput. 2006] to the block Krylov subspace setting for solving systems with multiple physical right-hand sides and for acceleration through the introduction of fictitious right-hand sides. We demonstrate the method's effectiveness in reducing the cost of a Newton iteration arising from fluid Density Functional Theory.
In Preparation
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Short-term recurrence Krylov Subsace Methods for Nearly-Hermitian Matrices
We analyze an short-term recurrence algorithm for solving nearly-Hermitian linear systems presented by Beckermann and Reichel [SIAM J. Matrix Anal. Appl. 2008], observing a critical instability making the method unsuitible for some problems. We introduce a different short-term recurrence method based on Krylov subspaces for the same classes of matrices.
Submitted for Publication
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The action of Hecke operators on hypergeometric functions
We study the spectrum of Hecke operators acting on hypergeometric functions. Polylogarithms appear as eigenfunctions.
Journal of the Australian Mathematical Society
Published 21 September, 2010
arXiv.org Preprint -
An analysis of the Landen transformation
Bachelor of Science Honors Thesis, Adviser: Victor Moll
Published May 2004
Work Experience
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Graduate Research Internship
Sandia National Labs, Albuquerque NM
Staff Mentor: Michael Parks
Developed a new linear solver suitable for deployment on next-generation high-end multicore systems. Implemented and deployed this algorithm into Sandia’s Trilinos Project, an open-source object-oriented software framework for the solution of large-scale, complex multi-physics engineering and scientific problems.
May 2011 - August 2011
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Research Assistantship
Temple University, Philadelphia PA
Advisor: Daniel Szyld
I study Krylov subspace iterative methods, specifically applications of subspace recycling.
2008-2011
Awards and Honors
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Dissertation Completion Fellowship
Temple University, Philadelphia, PA
Spring 2012 -
ICIAM 2011 Travel Award
ICIAM 2011, Vancouver BC
July 2011 -
Householder Symposium Travel Award
Householder Symposium, Tahoe City CA
June 2011 -
SIAM CSE Travel Award
SIAM Conference on Computational Science and Engineering, Reno NV
March 2011 -
Research Assistantship
Temple University, Philadelphia PA
2008-2011 -
Dean's Graduate Scholarship
Temple University, Philadelphia PA
2006-2008 -
Teaching Assistantship
Temple University, Philadelphia PA
2006-2008, 2011
Outreach Activities
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Mentor for Temple Undergraduate Math Modeling Competition
Fall 2011
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Graduate Student Peer Resource
Fall 2010 - Present
Workshops Attended
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2010 Gene Golub SIAM Summer School on Numerical Linear Algebra
June 7-18, 2010
Hotel Sierra Silvana, Selva di Fasano, Bari, Italy
Lectures on Minimizing Communication in Numerical Linear Algebra by James Demmel, Nonlinear Eigenvalue Problems: Analysis and Numerical Solution by Volker Mehrmann, From Matrix to Tensor: The Transition to Computational Multilinear Algebra by Charles van Loan, and Linear Algebra and Optimization by Margaret Wright -
Industrial Mathematical and Statistical Modeling Workshop for Graduate Students
July 20-28, 2010
Center for Research in Scientific Computation, Raleigh, NC, United States
Modeling Workshop in which we Studied Resource Issues Impacting National Security -
SIAG/LA-SIMUMAT International Summer School on Numerical Linear Algebra
June 21-25, 2008
International Center for Mathematical Meetings, Castro Urdiales, Cantabria, Spain
Lectures on Krylov Subspace Methods for Solving Linear Systems by Michael Eiermann, Matrix Methods in Data Mining by Lars Eldén, Mechanics and Linear Algebra by Richard B. Lehoucq, and Structured Eigenvalue Problems: Modern Theory and Computational Practice by David S. Watkins