E i g e n v a l u e C l i n i c

VIGRE Seminar, CAAM 699.005

Monday 1-2pm (DH 3076), Thursday 3-5pm (DH 2014)

The Eigenvalue Clinic is a weekly workshop where participants pose research problems related to applications of spectral theory in differential equations, numerical linear algebra, and control theory.

For more information, contact Mark Embree or Derek Hansen.

Summer 2010

Participants: Russell Carden, Mark Embree, Derek Hansen, A.J. Hergenroeder, Jeffrey Hokanson, Sharmaine Jennings, Josef Sifuentes, Gilbert Ymbert

25.	July 15: Mark Embree Transient behavior and quadratic eigenvalue problems Betcke, Higham, Mehrmann, Schröder and Tisseur NLEVP: A Collection of Nonlinear Eigenvalue Problems Download the collection here. Higham, Mackey, and Tisseur The conditioning of linearizations of matrix polynomials SIAM J. Matrix Anal. Appl. 28 (2007) 1005-1028. Higham, Mackey, Tisseur, Garvey Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems Int. J. Num. Methods Engrg. 73 (2008) 344-360. Code for wave operator with Castro-Cox damping: ccdamp.m (uses cheb.m) Code for energy norm matrices : engnorm.m (uses cheb.m and clencurt.m)

Spring 2010

Participants: Russell Carden, Mark Embree, Derek Hansen, Jeffrey Hokanson, Cosmin Ionita, Sanda Lefteriu, Josef Sifuentes

24.	April 19: Josef Sifuentes Preconditioning for Inverse Scattering Applications [thesis practice talk]


23.	March 25: Cosmin Ionita and Sanda Lefteriu Rational approximation of transfer functions Dieter Gaier Lectures on Complex Approximation Theory, Birkhäuser, 1987. A. I. Markushevich Theory of Functions of Complex Variable, Part 3, AMS Chelsea, 2005. Joseph Walsh Interpolation and Approximation by Rational Functions in the Complex Plane, 5th ed., AMS, 1969.


22.	February 22: Mark Embree and Josef Sifuentes Metrics for convergence of the spectrum of discretizations F. Chatelin Spectral Approximation of Linear Operators, Academic Press, 1983. M. Ahues, A. Largillier, B. V. Limaye Spectral Computations for Bounded Operators, Chapman and Hall, 2001.


21.	February 1: Mark Embree and Russell Carden The CS decomposition, angles between subspaces, subspace metrics G. W. Stewart and J.-g. Sun Matrix Perturbation Theory, Academic Press, 1990.


20.	January 25: Sanda Lefteriu Parametric model reduction


19.	January 21: Jeff Hokanson A Framework for System Identification

Fall 2009

Participants: Russell Carden, Mark Embree, Derek Hansen, Jeffrey Hokanson, Cosmin Ionita, Josef Sifuentes

18.	November 5: Josef Sifuentes Approximate deflation preconditioning J. Erhel, K. Burrage, B. Pohl Restarted GMRES preconditioned by deflation J. Comp. Applied Math. 69 (1996) 303-318. K. Burrage and J. Erhel On the performance of various adaptive preconditioned GMRES strategies Numer. Linear Algebra Appl. 101-121 (1998) 101-121. J. Frank, C. Vuik On the construction of deflation-based preconditioners SIAM J. Sci. Comp. 23 (2001) 442-462. Y. A. Erlangga and R. Nabben Deflation and balancing preconditioners for Krylov subspace methods applied to nonsymmetric matrices SIAM J. Matrix Anal. Appl. 30 (2008) 684-699. M. B. van Gijzen, Y. A. Erlangga, C. Vuik Spectral analysis of the discrete Helmholtz operator preconditioned with a shifted Laplacian SIAM J. Sci. Comput. 29 (2007) 1942-1958. L. Grammont and A. Largillier On ε-spectra and stability radii J. Comp. Applied Math. 147 (2002) 453-469. G. W. Stewart Error and perturbation bounds for subspaces associated with certain eigenvalue problems SIAM Review 15 (1973) 727-764.


17.	October 19: Russell Carden iFOV for normal matrices S. M. Malamud Inverse spectral problem for normal matrices and the Gauss-Lucas theorem Trans. Amer. Math. Soc. 357 (2005) 4043-4064. J. F. Queiró and A. L. Duarte Imbedding conditions for normal matrices Linear Algebra Appl. 430 (2009) 1806-1811.


16.	October 5: Cosmin Ionita Multiparameter linear systems


15.	September 24: Jeffrey Hokanson Eigenvalue estimates for rectangular pencils G. W. Stewart Perturbation theory for rectangular matrix pencils Linear Algebra Appl. 208-209 (1994) 297-301. T. G. Wright and L. N. Trefethen Pseudospectra of rectangular matrices IMA J. Num. Anal. 22 (2002) 501-519. G. Boutry, M. Elad, G. H. Golub, P. Milanfar The generalized eigenvalue problem for nonsquare pencils using a minimal perturbation approach SIAM J. Matrix Anal. Appl. 27 (2005) 582-601. F. Tisseur and N. J. Higham Structured pseudospectra for polynomial eigenvalue problems, with applications SIAM J. Matrix Anal. Appl. 23 (2001) 187-208.


14.	September 3: Russell Carden Ideal Arnoldi and trace-based eigenvalue bounds; polynomial numerical hulls H. Wolkowicz and G.P.H. Styan Bounds for eigenvalues using traces Linear Algebra Appl. 29 (1980) 471-506.


13.	August 26: Mark Embree Applying the Arnoldi algorithm directly to differential operators - The Chebfun Project at Oxford - cf_laplace.m: Chebfun code for inverse Arnoldi on the Laplacian - cf_advdiff.m: Chebfun code for inverse Arnoldi on an advection-diffusion operator - arnoldi_laplace.nb: Mathematica code for the Laplacian - arnoldi_laplace_gf.nb: Mathematica code for the Laplacian using the Green's function - arnoldi_advdiff_gf.nb: s l o w Mathematica code for the advection-diffusion operator

Summer 2009

Participants: Russell Carden, Mark Embree, Derek Hansen, Jeffrey Hokanson, Cosmin Ionita, Sanda Lefteriu, Josef Sifuentes, Gilbert Ymbert

12.	August 4: Gilbert Ymbert The Erlangga-Nabben preconditioner the Helmholtz equation


11.	July 21: Derek Hansen Kelvin-Voigt damping and greatest total energy minimization


10.	July 14: Sanda Lefteriu Loewner matrix techniques for determination of system order


9.	July 7: Russell Carden Approximate diagonalization and Davies's conjecture


8.	June 30: Josef Sifuentes Further investigation of the low-rank skew part of 1d scattering operators


7.	June 23: Mark Embree Spectral variation for normal matrices (Krause's example)


6.	June 16: Derek Hansen Optimizing the greatest total energy in a viscously damped vibrating string


5.	June 9: Cosmin Ionita Loewner matrix methods for system realization and exponential data fitting


4.	June 2: Jeffrey Hokanson Singular matrix pencils arising in exponential data fitting


3.	May 26: Russell Carden Inclusion regions for Ritz values (iFOVk problem) (Russell poses the iFOVk problem in his article in Inverse Problems.)


2.	May 19: Josef Sifuentes Spectral problems in acoustic scattering


1.	May 12: Mark Embree Model reduction and higher order discretizations (Arnoldi on operators)