I am working with Vadim Olshevsky in structured
scientific computing. My current projects are on the design of fast and accurate algorithms for structured matrices, particularly matrices with quasiseparable structure and their applications to eigenvalue computations, algebraic coding theory and digital filter design.
Research Interests
My current research interests include:
Scientific computing and numerical linear algebra.
Matrix theory, structured matrices, matrices with quasiseparable structure.
Indefinite inner product spaces.
Signal processing and control theory.
Algebraic coding theory.
NEW
Publications
Using unitary Hessenberg matrices to factor projectors (with V. Olshevsky, A. Phillips), in preparation
Fast algorithms for multiplication of a quasiseparable matrix by a vector (with V. Olshevsky, M. Stewart), in preparation
Signal Flow Graph Approach to Inversion of (H,m)-Quasiseparable Vandermonde Matrices and New Filter Structures (with V. Olshevsky, P. Zhlobich), Linear Algebra and its Applications, Volume 432, Issue 8, 1 April 2010, Pages 2032-2051 (2010)
A quasiseparable approach to five-diagonal CMV and companion matrices (with V. Olshevsky, P. Zhlobich), in preparation
Presentations
Stability of Methods for Quasiseparable Matrices, Minisymposium on Structured Matrix Computations, SIAM Conference on Computational Science and Engineering, Reno, NV, USA (2011) http://www.siam.org/meetings/cse11/index.php
Arbitrary Order Hessenberg Quasiseparable Matrices and Polynomials, Three-Part Minisymposium on Quasiseparable Matrices and Polynomials (minisymposium speaker and co-organizer), SIAM Applied Linear Algebra 2009, Monterey, CA, USA (2009) http://www.siam.org/meetings/la09/
Publications
In Preparation
A QR algorithm for out-of-band quasiseparable matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky), in preparation
A quasiseparable approach to five-diagonal CMV and companion matrices (with V. Olshevsky, P. Zhlobich), in preparation
Using unitary Hessenberg matrices to factor projectors (with V. Olshevsky, A. Phillips), in preparation
Fast algorithms for multiplication of a quasiseparable matrix by a vector (with V. Olshevsky, M. Stewart), in preparation
Submitted
Classifications of three-term and two-term recurrence relations via subclasses of quasiseparable matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky), submitted to SIAM Journal of Matrix Analysis (SIMAX)
A Fast Traub-like inversion algorithm for Hessenberg order one quasiseparable Vandermonde matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky, E. Tyrtyshnikov), submitted to Journal of Complexity
2010
Signal Flow Graph Approach to Inversion of (H,m)-Quasiseparable Vandermonde Matrices and New Filter Structures (with V. Olshevsky, P. Zhlobich), Linear Algebra and its Applications, Volume 432, Issue 8, 1 April 2010, Pages 2032-2051 (2010)
2009
A Traub-like algorithm for Hessenberg-quasiseparable-Vandermonde matrices of arbitrary order (with Y. Eidelman, I. Gohberg, V. Olshevsky, E. Tyrtyshnikov, P. Zhlobich), Journal of Integral Equations and Operator Theory, Georg Heinig Memorial Volume, Birkhauser Verlag (2009)
Classifications of recurrence relations via subclasses of (H,k)-quasiseparable matrices (with V. Olshevsky, P. Zhlobich), Numerical Linear Algebra in Signals, Systems and Control, Lecture Notes in Electrical Engineering, Springer-Verlag, (2009)
A fast Bjorck-Pereyra-type algorithm for solving Hessenberg-quasiseparable-Vandermonde systems (with Y. Eidelman, I. Gohberg, I. Koltracht, V. Olshevsky), SIAM. J. Matrix Anal. & Appl., Volume 31, Issue 2, pp. 790-815 (2009) (2009)
2008
Computations with quasiseparable polynomials and matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky), Theoretical Computer Science, Volume 409, Issue 2, 17 December 2008, Pages 158-179 (2008)
Lipschitz stability of canonical Jordan bases of H-selfadjoint matrices under structure-preserving perturbations (with V. Olshevsky, U. Prasad), Linear Algebra and its Applications, Volume 428, Issues 8-9, 15 April 2008, Pages 2130-2176 (2008)
Ranks of Hadamard Matrices and Equivalence of Sylvester Hadamard and Pseudo-Noise Matrices (with V. Olshevsky, L. Sakhnovich), Recent Advances in Matrix and Operator Theory, 35--46, Oper. Theory Adv. Appl., 179, Birkhauser, Basel, (Conference version appeared in: Proc. SPIE Vol. 5910.), (2008)
2007
A Bjorck-Pereyra-type algorithm for Szego-Vandermonde matrices based on properties of unitary Hessenberg matrices (with Y. Eidelman, I. Gohberg, I. Koltracht, V. Olshevsky), Linear Algebra and Applications, Volume 420, Issues 2-3 pp. 634-647 (2007)
Talks
2011
Stability of Methods for Quasiseparable Matrices, Minisymposium on Structured Matrix Computations, SIAM Conference on Computational Science and Engineering, Reno, NV, USA (2011) http://www.siam.org/meetings/cse11/index.php
Minisymposium on Large Scale Matrix Computation, AMS Spring Southeastern Sectional Meeting in Lexington, KY, USA, March 27-28, 2010 (Meeting #1057) (2010) http://www.ams.org/amsmtgs/2162_program.html
2009
Arbitrary Order Hessenberg Quasiseparable Matrices and Polynomials, Three-Part Minisymposium on Quasiseparable Matrices and Polynomials (minisymposium speaker and co-organizer), SIAM Applied Linear Algebra 2009, Monterey, CA, USA (2009) http://www.siam.org/meetings/la09/
Arbitrary Order Hessenberg Quasiseparable Matrices and Polynomials, Northern Illinois University Linear Algebra Meeting 2009, DeKalb, IL, USA (2009) http://www.math.niu.edu/LA09/
2008
Classifications of quasiseparable matrices in terms of recurrence relations, Structured Linear Algebra Problems: Analysis, Algorithms, and Applications 2008 - Cortona, Italy (2008) http://www.dm.unipi.it/~cortona08
Fast algorithms for polynomial-Vandermonde matrices related to quasiseparable matrices, Minisymposium on Interpolation Problems, Eighteenth International symposium on Mathematical Theory of Networks and Systems (MTNS2008) (2008) http://www.cpe.vt.edu/mtns08/
Fast algorithms for polynomial-Vandermonde matrices related to quasiseparable matrices, Minisymposium on Structured Matrices, IWOTA 2008 - Williamsburg, VA, USA (2008) http://www.math.wm.edu/~vladi/IWOTA/IWOTA2008.htm
Eigenproblems for quasiseparable matrices, Minisymposium on Eigenproblems: Theory and Computation, ILAS 2008 - Cancun, Mexico (2008) http://star.izt.uam.mx/ILAS08/
Quasiseparable matrices and polynomials, Hans Schneider 80th Birthday Meeting, UConn, Storrs, CT (2007)
Fast algorithms for polynomial Vandermonde matrices related to quasiseparable matrices, Minisymposium on Structured matrix algorithms: complexity and stability, ICIAM 2007 - Zurich, Switzerland - 6th International Congress on Industrial and Applied Mathematics (2007)
2006
Fast algorithms for polynomial Vandermonde matrices related to quasiseparable matrices, Minisymposium on Structured Matrices and Fast Algorithms, SIAM 2006 - Boston, MA (2006)
2005
The Equivalence of Pseudo-noise and Hadamard-Sylvester matrices, ILAS 2005 - Regina, Canada (2005)
The generalized Bjorck-Pereyra algorithm for Szego-Vandermonde matrices based on properties of unitary Hessenberg matrices, ILAS 2005 - Regina, Canada (2005)
A Parker-Forney-Traub like algorithm for quasiseparable-Hessenberg-Vandermonde matrices, Minisymposium on Structured Matrices, IWOTA 2005 - Storrs, CT, USA (2005)
The Equivalence of Pseudo-noise and Hadamard-Sylvester matrices, SPIE 2005 - San Diego, CA (2005)
2004
Introduction to Linear Codes, Series in Linear Codes, SIGMA Seminar, University of Connecticut (2004)
The Equivalence of Pseudo-noise and Hadamard-Sylvester matrices, ILAS 2004 - Coimbra, Portugal (2004)
