Professor, Department of Mathematics

Leader, Computational Modeling and Data Analytics (CMDA) division

Associate Director, Virginia Tech Smart Infrastructure Laboratory

*Office:* 575 McBryde Hall (VT map)

*Mailing Address:* 225 Stanger Street 0123, Virginia Tech, Blacksburg, Virginia 24061

*Email:* embree@vt.edu

*Telephone:* (540) 231-9592

### research interests

### upcoming events

Leader, Computational Modeling and Data Analytics (CMDA) division

Associate Director, Virginia Tech Smart Infrastructure Laboratory

- Numerical analysis, especially matrix computations
- Data analytics for smart buildings
- Dynamics and perturbation theory for non-self-adjoint operators
- Spectral theory for Schrödinger operators

- Householder Symposium XX, 18-23 June 2017, Blacksburg, Virginia

*Applications accepted until 31 October 2016*. - International Linear Algebra Society meeting, 24-28 July 2017, Ames, Iowa
- Workshop on Crouzeix's Conjecture, 31 July - 4 August 2017, AIM, San Jose, California

*Applications accepted until 31 January 2017*.

*
In Spring 2014, Virginia Tech launched this new undergraduate major,
a collaboration between the departments of
Computer Science, Mathematics, and Statistics.
Faculty have developed eight new courses for the major.
Other departments have added specialized options for students seeking
to apply CMDA skills in particular applications.
The first class will graduate in May 2017.
As of January 2017, more than 300 students have declared the CMDA major.
*

- Flowcharts for the
*standard option*,*Physics option*,*Economics option*. - Suggestions for
*capstone projects*for Fall 2017 are welcome. - For further details, see the CMDA webpage.

- MATH 5524: Matrix Theory [Monday/Wednesday/Friday, 1:10-2:20pm, McBryde 328]
- Office Hours: Monday 4-5:30pm, Thursday 1:30-3:00pm, and by appointment

Pseudospectra and Nonnormal Dynamical Systems (4th Elgersburg School, March 2012)

- Lecture notes on Numerical Analysis (for MATH 5466 at Virginia Tech)
- Physical Laboratory manual to accompany undergraduate Matrix Analysis

(with S. J. Cox, J. M. Hokanson, and others)

- Data from vibrating beaded strings for solving the inverse eigenvalue problem described
in
*this article*. - CMDA 3606: Mathematical Modeling II (Spring 2014)
- CMDA 4604: Intermediate Topics in Mathematical Modeling (Fall 2015)
- CMDA 4864: Capstone Project Course (Fall 2016)
- CAAM 440: Applied Matrix Analysis (Spring 2012 at Rice)

- Jonathan Baker

*Lyapunov equations, convex optimization, data analytics*(PhD in progress)

Jonathan contributes to the American Math Society's grad student blog - Russell Carden

*Arnoldi convergence, Ritz values (1, 2), inverse field of values problems*(PhD 2011) - Jeffrey Hokanson

*exponential data fitting, inverse eigenvalue problems*(PhD 2013) - John Sabino

Thesis:*Solution of Large-Scale Lyapunov Equations via the Block Modified Smith Method*(PhD 2006) - Josef Sifuentes

Thesis:*Preconditioned Iterative Methods for Inhomogeneous Acoustic Scattering Applications*(PhD 2010)

Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and OperatorsLloyd N. Trefethen and Mark Embree Princeton University Press, 2005. Section 1 in PDF from Princeton University Press Princeton; amazon.com; Barnes & Noble; AddAll search. |

EigTool, Tom Wright's excellent code for computing
pseudospectra, is now on GitHub.

Contributions are welcome!

*Click on a linked title for further details.*

- Spectra of discrete two-dimensional periodic Schrödinger operators with small potentials

M. Embree and J. Fillman

Preprint: arXiv:1701.00863 [math.SP]

- Weighted inner products for GMRES and Arnoldi iterations

M. Embree, R. B. Morgan, and H. V. Nguyen

Preprint: arXiv:1607.00255 [math.NA]

- Pseudospectra of matrix pencils for transient analysis
of differential-algebraic equations

M. Embree and B. Keeler

Preprint: arXiv:1601.00044 [math.NA]

- "Fast singular value decay for Lyapunov solutions with nonnormal coefficients

J. Baker, M. Embree, and J. Sabino

*SIAM J. Matrix Anal. Appl.*36 (2015) 656-668. (Copyright SIAM, 2015)

Preprint: arXiv:1410.8741 [math.NA]

- "Spectral approximation for quasiperiodic Jacobi operators"

C. Puelz, M. Embree, and J. Fillman

*Integral Equations Operator Theory*82 (2015) 533-554.

(Preprint: arXiv:1408.0370 [math.SP])

- "A DEIM induced CUR factorization"

D. C. Sorensen and M. Embree

*SIAM J. Sci. Comp.*38 (2016) A1454-A1482. (Copyright SIAM, 2016)

arXiv:1407.5516 [math.NA]

- "Spectral properties of Schrödinger operators arising in the study of quasicrystals"

D. Damanik, M. Embree, A. Gorodetski

In*Mathematics of Aperiodic Order*, pages 307-370; Kellendonk, Lenz, Savinien, eds., Springer, 2015

(Preprint: arXiv:1210.5753 [math-ph])

- "The stability of GMRES convergence, with application to approximate deflation preconditioning"

J. A. Sifuentes, M. Embree, and R. B. Morgan

*SIAM J. Matrix Anal. Appl.*34 (2013) 1066-1088. (Copyright SIAM, 2013)

- "Ritz value localization for non-Hermitian matrices"

R. Carden and M. Embree

*SIAM J. Matrix Anal. Appl.*33 (2012) 1320-1338. (Copyright SIAM, 2012)

- "Short-term recurrence Krylov subspace methods for nearly Hermitian matrices"

M. Embree , J. A. Sifuentes, K. M. Soodhalter, D. B. Szyld, and F. Xue

*SIAM J. Matrix Anal. Appl.*33 (2012) 480-500. (Copyright SIAM, 2012)

- "Reconstructing an even damping from a single spectrum"

S. J. Cox and M. Embree

*Inverse Problems*27 (2011) 035012 (18pp).

- "One can hear the composition of a string: experiments with an inverse eigenvalue problem"

S. J. Cox, M. Embree, and J. Hokanson

*SIAM Review*54 (2012) 157-178. (Copyright SIAM, 2012)

Additional data sets are available at www.caam.rice.edu/~beads.

- "Dynamical systems and non-Hermitian iterative eigensolvers"

M. Embree and R. B. Lehoucq

*SIAM J. Num. Anal.*47 (2009) 1445-1473. (Copyright SIAM, 2009)

- "The fractal dimension of the spectrum of the Fibonacci Hamiltonian"

D. Damanik, M. Embree, A. Gorodetski, and S. Tcheremchantsev

*Commun. Math. Phys.*280 (2008) 499-516.

- "The Arnoldi eigenvalue iteration with exact shifts can fail"

*SIAM J. Matrix Anal. Appl.*31 (2009) 1-10. (Copyright SIAM, 2009)

- "Parallel solution of large-scale free surface viscoelastic flows
via sparse approximate inverse preconditioning"

Z. Castillo, X. Xie, D. C. Sorensen, M. Embree, and M. Pasquali

*J. Non-Newtonian Fluid Mech.*157 (2009) 44-54.

- "The role of the penalty in the local discontinuous Galerkin method for
Maxwell's eigenvalue problem"

T. Warburton and Mark Embree

*Comp. Methods Appl. Mech. Eng.*195 (2006) 3205-3323.

- "Convergence of polynomial restart Krylov methods for eigenvalue computation

Christopher A. Beattie, Mark Embree, D. C. Sorensen

*SIAM Review*47 (2005) 492-515. (Copyright SIAM, 2005)

- "Convergence of restarted Krylov subspaces to invariant subspaces"

Christopher Beattie, Mark Embree, John Rossi

*SIAM J. Matrix Anal. Appl.*25 (2004) 1074-1109. (Copyright SIAM, 2004)

- "The tortoise and the hare restart GMRES"

*SIAM Review*45 (2003) 259-266. (Copyright SIAM, 2003)

- "The spectra of large Toeplitz band matrices with a randomly perturbed entry"

Albrecht Böttcher, Mark Embree, V. I. Sokolov

*Math. Comp.*72 (2003), 1329-1348.

- "On large Toeplitz band matrices with an uncertain block"

Albrecht Böttcher, Mark Embree, V. I. Sokolov

*Linear Algebra Appl.*366 (2003), 87-97.

- "Spectral approximation of banded Laurent matrices with localized random perturbations"

Albrecht Böttcher, Mark Embree, Marko Lindner

*Integral Equations Operator Theory*42 (2002), 142-165. (Copyright Birkhäuser, 2002)

- "Piecewise continuous Toeplitz matrices and operators:
slow approach to infinity

Albrecht Böttcher, Mark Embree, Lloyd N. Trefethen

*SIAM J. Matrix Anal. Appl.*24 (2002) 484-489. (Copyright SIAM, 2002)

- "Infinite Toeplitz and Laurent matrices with localized impurities"

Albrecht Böttcher, Mark Embree, V. I. Sokolov

*Linear Algebra Appl.*343-344 (2002), 101-118.

- "Generalizing eigenvalue theorems to pseudospectra theorems"

Mark Embree and Lloyd N. Trefethen

*SIAM J. Sci. Comp.*23 (2001) 583-590. (Copyright SIAM, 2001)

- "Spectra, pseudospectra, and localization for random bidiagonal matrices"

Lloyd N. Trefethen, Marco Contedini, Mark Embree

*Comm. Pure Applied Math.*54 (2001) 595-623.

- "How descriptive are GMRES convergence bounds?"

Oxford University Computing Laboratory Numerical Analysis Report 99/08, June 1999.

- "Green's functions for multiply connected domains via conformal mapping"

Mark Embree and Lloyd N. Trefethen

*SIAM Review*41 (1999) 745-761.

- "Growth and decay of random Fibonacci sequences"

Mark Embree and Lloyd N. Trefethen

*Proc. Roy. Soc. London Series A*455 (1999) 2471-2485.