Mark Embree Professor, Computational and Applied Mathematics Co-director, Rice Center for Engineering Leadership Rice University 6100 Main Street - MS 134 Houston, Texas 77005-1892 embree@rice.edu tel. (713) 348-6160 fax. (713) 348-5318 Duncan Hall 3019/ Abercrombie A101 Research Interests Krylov subspace methods for linear systems and eigenvalue problems; Nonnormal operators and spectral perturbation theory;     -See the Pseudospectra Gateway and the EigTool package Toeplitz matrices, random matrices, damped wave operators Teaching Spring 2013 CAAM 496, Senior Design (Mondays, 4-5pm) CAAM 699, Eigenvalue Clinic (Mondays, 11am-12pm) - Office Hours: by appointment [Abercrombie A101] Some Past Classes CAAM 440 - Applied Matrix Analysis (Spring 2012) CAAM 453/553 - Numerical Analysis I (Fall 2009) with lecture notes CAAM 651 - Numerical Methods for Dimension Reduction of Dynamical Systems (w/Dan Sorensen) Physical Laboratory manual to accompany undergraduate Matrix Analysis (with S. J. Cox, J. M. Hokanson, and others) See also inverse eigenvalue data for beaded strings. Ph.D. Students, past and present Russell Carden: Arnoldi convergence, Ritz values (1, 2), inverse field of values problems (PhD 2011) Jeffrey Hokanson: damped wave operators, exponential data fitting, inverse eigenvalue problems (PhD expected 2012) John Sabino: Solution of Large-Scale Lyapunov Equations via the Block Modified Smith Method (PhD 2006). Josef Sifuentes: Preconditioned Iterative Methods for Inhomogeneous Acoustic Scattering Applications (PhD 2010). Book   Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators Lloyd N. Trefethen and Mark Embree Princeton University Press, 2005. Section 1 in PDF from Princeton University Press Princeton; amazon.com; Barnes & Noble; AddAll. Slides Pseudospectra and Nonnormal Dynamical Systems (4th Elgersburg School, March 2012) Lecture 1, 2, 3, 4, 5 Misconvergence of Arnoldi Eigenvalue Iterations (IWASEP, June 2006) Pseudospectra of Piecewise Continuous Toeplitz Matrices (IWOTA, August 2002) Restarted GMRES Dynamics (Householder Symposium XV, June 2002) Papers and technical reports "Spectral properties of Schrödinger operators arising in the study of quasicrystals" D. Damanik, M. Embree, A. Gorodetski Rice University CAAM Department Technical Report TR12-21 (October 2012) "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) "The stability of GMRES convergence, with application to approximate deflation preconditioning" J. A. Sifuentes, M. Embree, and R. B. Morgan Rice University CAAM Department Technical Report TR11-13 (revised January 2013) "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) gzipped postscript (833 KBytes), pdf (1.0 MBytes). "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.