Mark Embree Professor Computational and Applied Mathematics 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 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 CAAM 453/553 - Numerical Analysis I - Office Hours: Monday 10-11am, Thursday 1:30-3pm Eigenvalue Clinic Physical Laboratory manual to accompany undergraduate Matrix Analysis (with S. J. Cox, J. M. Hokanson, and others) 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 "Misconvergence of Arnoldi Eigenvalue Iterations (IWASEP, June 2006) pdf (2.6 MBytes) "Pseudospectra of Piecewise Continuous Toeplitz Matrices" (IWOTA, August 2002) pdf (2.41 MBytes) "Restarted GMRES Dynamics" (Householder Symposium XV, June 2002) pdf (2.62 MBytes) Papers and technical reports "One can hear the composition of a string: experiments with an inverse eigenvalue problem" S. J. Cox, M. Embree, and J. Hokanson Rice University CAAM Department Technical Report TR08-10 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 Fibonaaci sequences" Mark Embree and Lloyd N. Trefethen Proc. Roy. Soc. London Series A 455 (1999) 2471-2485.