Brian Sutton

Brian Sutton is Associate Professor of Mathematics at Randolph-Macon College in Ashland, VA. His primary research areas are numerical linear algebra and random matrix theory. He is the First Place recipient of the Fourteenth Leslie Fox Prize in numerical analysis for his work on computing the CS (Cosine-Sine) matrix decomposition, and his current work on the CS decomposition is funded by NSF grant DMS-0914559. With Alan Edelman, he founded the stochastic operator approach to random matrix theory, which reinterprets finite random matrices as discretizations of a select few continuous operators, moving the field into the domain of functional analysis. At Randolph-Macon, Brian has taught courses on numerical analysis, differential equations, probability, and statistics, as well as an interdisciplinary course on epidemiology.

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Curriculum vitae

Contact

Copley 235

Department of Mathematics, Randolph-Macon College, PO Box 5005, Ashland, VA 23005

Current courses

Software

Publications and preprints

• The fundamental CS decomposition
  • In preparation.
• Divide and conquer the CS decomposition
  • Submitted for publication.
• Stable computation of the CS decomposition: simultaneous bidiagonalization
  • SIAM J. Matrix Anal. Appl. 33 (2012), no. 1, 1–21.
• On the minimum semidefinite rank of a simple graph
  • With Matthew Booth, Philip Hackney, Benjamin Harris, Charles R. Johnson, Margaret Lay, Terry D. Lenker, Lon H. Mitchell, Sivaram K. Narayan, and Amanda Pascoe. Linear Multilinear Algebra 59 (2011), no. 5, 483–506.
• Computing the complete CS decomposition
  • Computing the complete CS decomposition. Numer. Algorithms. 50 (2009), no. 1, 33–65.
• Implicit construction of multiple eigenvalues for trees
  • With Charles R. Johnson and Andrew J. Witt. Implicit construction of multiple eigenvalues for trees. Linear Multilinear Algebra 57 (2009), no. 4, 409–420.
• The beta-Jacobi matrix model, the CS decomposition, and generalized singular value problems
  • With Alan Edelman. The beta-Jacobi matrix model, the CS decomposition, and generalized singular value problems. Found. Comput. Math. 8 (2008), no. 2, 259–285.
• On the minimum rank of a positive semidefinite matrix with a given graph
  • With Matthew Booth, Philip Hackney, Benjamin Harris, Charles R. Johnson, Margaret Lay, Lon H. Mitchell, Sivaram K. Narayan, Amanda Pascoe, Kelly Steinmetz, and Wendy Wang. On the minimum rank of a positive semidefinite matrix with a given graph. SIAM J. Matrix Anal. Appl. 30 (2008), no. 2, 731–740.
• From random matrices to stochastic operators
  • With Alan Edelman. From random matrices to stochastic operators. J. Stat. Phys. 127 (2007), no. 6, 1121–1165.
• The Stochastic Operator Approach to Random Matrix Theory
  • The Stochastic Operator Approach to Random Matrix Theory. Ph.D. thesis, Massachusetts Institute of Technology, 2005.
• Tails of condition number distributions
  • With Alan Edelman. Tails of condition number distributions. SIAM J. Matrix Anal. Appl. 27 (2005), no. 2, 547–560.
• Hermitian matrices, eigenvalue multiplicities, and eigenvector components
  • With Charles R. Johnson. Hermitian matrices, eigenvalue multiplicities, and eigenvector components. SIAM J. Matrix Anal. Appl. 26 (2004/05), no. 2, 390–399.
• On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph
  • With Charles R. Johnson, António Leal Duarte, Carlos M. Saiago, and Andrew J. Witt. On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph. Special issue on nonnegative matrices, M-matrices and their generalizations (Oberwolfach, 2000). Linear Algebra Appl. 363 (2003), 147–159.
• Identification problem for the wave equation with Neumann data input and Dirichlet data observations
  • With Xiaobing Feng, Suzanne Lenhart, Vladimir Protopopescu, and Lizabeth Rachele. Identification problem for the wave equation with Neumann data input and Dirichlet data observations. Nonlinear Anal. 52 (2003), no. 7, 1777–1795.

Presentations

• Computing the complete CS decomposition
• From random matrices to stochastic operators
• Tossing a coin: It's harder than it looks, based on Daniel W. Stroock's "Doing analysis by tossing a coin"
• From Photoshop to programming languages: an algebraic approach to computation (PDF)
• Random matrix theory: beyond real and complex (PS)
• The mind-body problem in computation (PS)
• Mmm, lambda curry (PS)