Welcome to Merico Argentati's Home Page!

Mathematician/Engineer

Department of Mathematics, University of Colorado at Denver

P.O. Box 173364, Campus Box 170, Denver, CO 80217-3364.
Street Address: 1250 14th St. Room 644, Denver CO 80202
Phone: (303) 556-8442. Fax: (303) 556-8550
E-mail: merico.argentati@ucdenver.edu

My Resume: Resume

Work/Research Interests:

• Scientific computing, computational math and modeling/analysis of engineering and business problems.
• Efficient and robust implementation using c-language, Fortran, Matlab, Excel, etc.
• Parallel implementation of algorithms.
• Numerical analysis including general solvers, finite differences, finite elements and CFD
• Iterative solution of large sparse linear systems and eigenproblems
• Bounds for eigenvalues, stability and perturbations.

Education:

• 2003: Ph.D. in Applied Mathematics, University of Colorado at Denver, Colorado. Numerical analysis/scientific computing. Ph.D. Thesis: Principal Angles Between Subspaces As Related To Rayleigh Quotient And Rayleigh Ritz Inequalities With Applications To Eigenvalue Accuracy And An Eigenvalue Solver, Thesis Advisor: Andrew Knyazev.
• 1977: M.S. in Applied Mathematics, University of Colorado at Boulder, Colorado.
• 1971: M.S. in Aerospace Engineering, University of California at San Diego, California. Optimization and control theory. M.S. Thesis: A numerical study of direct search techniques in unconstrained minimization.
• 1970: B.S. in Mechanical Engineering, Worcester Polytechnic Institute, Worcester, Massachusetts.

Some Recent Talks:

• Using the Karush-Kuhn-Tucker Conditions to Analyze the Convergence Rate of Preconditioned Eigenvalue Solvers, UCD Computational Mathematics Colloquium, October 18, 2010.
• Majorization-based convergence rate bounds for subspace iterations and the block Lanczos method, 2008 Copper Mountain Conference on Iterative Methods.
• A Priori Error Bounds for Eigenvalues Approximated by Ritz Values, 2006 Copper Mountain Conference on Iterative Methods.
• Majorization for Changes in Ritz Values and Canonical Angles Between Subspaces, 2005 ILAS Conference, Regina, Saskatchewan.
• Majorization for Changes in Principal Angles Between Subspaces, UCD Computational Mathematics Colloquium, 2004.

U.S. Patents:

• Control data link format utilizing CRC error detection, Merico E. Argentati, et al, U.S. patent #6,412,093, assignee: Lucent Technologies Inc. (Murray Hill, NJ), issued June 25, 2002.
• Network congestion measurement method and apparatus, Merico E. Argentati, U.S. patent #5,754,120, assignee: Lucent Technologies Inc. (Murray Hill, NJ), issued May 19, 1998.

Publications:

• Merico E. Argentati, Principal Angles Between Subspaces As Related To Rayleigh Quotient And Rayleigh Ritz Inequalities With Applications To Eigenvalue Accuracy And An Eigenvalue Solver, PhD thesis, University of Colorado at Denver, 2003, Thesis Advisor: Andrew Knyazev.
• A. V. Knyazev, A. Jujunashvilia, M. E. Argentati, Angles Between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods, Journal of Functional Analysis, accepted, 2010.
• A. V. Knyazev, M. E. Argentati, Rayleigh-Ritz majorization error bounds with applications to FEM , SIAM Journal on Matrix Analysis and Applications (SIMAX), Vol. 31 (2010), No. 3, pp. 1521-1537.
• M. E. Argentati, A. V. Knyazev, C. C. Paige, and I. Panayotov Bounds on changes in Ritz values for a perturbed invariant subspace of a Hermitian matrix, SIAM Journal on Matrix Analysis and Applications (SIMAX), Vol. 30 (2008), No. 2, pp. 548-559.
• A. V. Knyazev, I. Lashuk, M. E. Argentati, and E. Ovchinnikov, Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc, SIAM Journal on Scientific Computing (SISC), Vol. 29 (2007), No. 5, pp. 2224-2239.
• I. Lashuk, M. E. Argentati, E. Ovchinnikov and A. V. Knyazev, Preconditioned Eigensolver LOBPCG in hypre and PETSc. In Lecture Notes in Computational Science and Engineering, v. 55 (2007) (Proceedings of the 16th International Conference on Domain Decomposition Methods. 2005). Editors: O.~B. Widlund and D.~E. Keyes, pages 635-642, ISBN: 3-540-34468-3.
• A. V. Knyazev and M. E. Argentati, Majorization for Changes in Angles Between Subspaces, Ritz values, and graph Laplacian spectra, SIAM Journal on Matrix Analysis and Applications (SIMAX), Vol. 29 (2006), No. 1, pp. 15-32.
• A. V. Knyazev and M. E. Argentati, On Proximity of Rayleigh Quotients for Different Vectors and Ritz Values Generated by Different Trial Subspaces. Linear Algebra and Its Applications. Vol. 415 (2006), Issue 1, pp. 82-95.
• A. V. Knyazev and M. E. Argentati, Implementation of a Preconditioned Eigensolver Using Hypre, Technical report UCD-CCM 220, April 2005, at the Center for Computational Mathematics, University of Colorado at Denver.
• A. V. Knyazev and Merico E. Argentati, Principal Angles between Subspaces in an A-Based Scalar Product: Algorithms and Perturbation Estimates, SIAM Journal on Scientific Computing (SISC), Vol. 23 (2002), No. 6, pp. 2009-2041.

Miscellaneous:

• Reviewer/Referee for SIAM Journal on Matrix Analysis and Applications (SIMAX)
• Trip leader for Colorado Mountain Club

Some Relevant Links:

• NA-NET
• SIAM (Society for Industrial and Applied Mathematics)
• ILAS (International Linear Algebra Society)
• MathSciNet (Skyline Access)
• Guide to Available Mathematical Software (GAMS)
• NETLIB (BLAS, LAPACK, CLAPACK) )
• ARPACK
• ABINIT
• Cygwin
• Wikipedia
• PlanetMath
• WolframMathWorld
• WolframAlpha
• St.Andrews Mathematicians
• Women Mathematicians
• Matrix Reference Manual
• ALGLIB NET (C#)
• Jacobi-Davidson Gateway
• Math Pages
• Math Quotes
• Miscellaneous Usefull Information
• Cornell University Libarary (arXiv.org)
  Majorization for Changes in Angles Between Subspaces, Ritz Values, and Graph Laplacian Spectra,
  Bounds on changes in Ritz values for a perturbed invariant subspace of a Hermitian matrix,
  Angles Between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods,
  Rayleigh-Ritz majorization error bounds with applications to FEM and subspace iterations

Some of My Favorite Quotes: Quotes

Last Upated: 10/16/2010 by Merico Argentati