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
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)
A Traub-like algorithm for Hessenberg-quasiseparable-Vandermonde matrices of arbitrary order (with Y. Eidelman, I. Gohberg, V. Olshevsky, E. Tyrtyshnikov, P. Zhlobich), Georg Heinig Memorial Volume, (V. Olshevsky, editor), Birkhauser Verlag to appear, 2008
Computations with quasiseparable polynomials and matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky), Theoretical Computer Science, Volume 409, Issues 2-3, Pages 158-179 (2008)
Classifications of recurrence relations via subclasses of (H,k)-quasiseparable matrices (with V. Olshevsky, P. Zhlobich), accepted, Numerical Linear Algebra in Signals, Systems and Control, Springer-Verlag
Presentations
Classifications of quasiseparable matrices in terms of recurrence relations (with V. Olshevsky), 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 (with V. Olshevsky), 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 (with V. Olshevsky), Minisymposium on Structured Matrices, IWOTA 2008 - Williamsburg, VA, USA (2008) http://www.math.wm.edu/~vladi/IWOTA/IWOTA2008.htm
Eigenproblems for quasiseparable matrices (with V. Olshevsky), Minisymposium on Eigenproblems: Theory and Computation, ILAS 2008 - Cancun, Mexico (2008) http://star.izt.uam.mx/ILAS08/
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)
Algebraic Coding Theory
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)
Numerical Linear Algebra
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)
A Traub-like algorithm for Hessenberg-quasiseparable-Vandermonde matrices of arbitrary order (with Y. Eidelman, I. Gohberg, V. Olshevsky, E. Tyrtyshnikov, P. Zhlobich), Georg Heinig Memorial Volume, (V. Olshevsky, editor), Birkhauser Verlag to appear, 2008
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
A fast Bjorck-Pereyra-type algorithm for solving Hessenberg-quasiseparable-Vandermonde systems (with Y. Eidelman, I. Gohberg, I. Koltracht, V. Olshevsky), submitted to SIAM Journal of Matrix Analysis (SIMAX)
A QR algorithm for out-of-band quasiseparable matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky), 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
Orthogonal Polynomials
Computations with quasiseparable polynomials and matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky), Theoretical Computer Science, Volume 409, Issues 2-3, Pages 158-179 (2008)
Classifications of recurrence relations via subclasses of (H,k)-quasiseparable matrices (with V. Olshevsky, P. Zhlobich), accepted, Numerical Linear Algebra in Signals, Systems and Control, Springer-Verlag
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)
Signal Flow Graph Approach to Inversion of (H,m)-Quasiseparable Vandermonde Matrices and New Filter Structures (with V. Olshevsky, P. Zhlobich), in preparation
Talks
Invited Minisymposium Talks
Classifications of quasiseparable matrices in terms of recurrence relations (with V. Olshevsky), 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 (with V. Olshevsky), 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 (with V. Olshevsky), Minisymposium on Structured Matrices, IWOTA 2008 - Williamsburg, VA, USA (2008) http://www.math.wm.edu/~vladi/IWOTA/IWOTA2008.htm
Eigenproblems for quasiseparable matrices (with V. Olshevsky), Minisymposium on Eigenproblems: Theory and Computation, ILAS 2008 - Cancun, Mexico (2008) http://star.izt.uam.mx/ILAS08/
Fast algorithms for polynomial Vandermonde matrices related to quasiseparable matrices (with V. Olshevsky), Minisymposium on Structured matrix algorithms: complexity and stability, ICIAM 2007 - Zurich, Switzerland - 6th International Congress on Industrial and Applied Mathematics (2007)
Fast algorithms for polynomial Vandermonde matrices related to quasiseparable matrices (with V. Olshevsky), Minisymposium on Structured Matrices and Fast Algorithms, SIAM 2006 - Boston, MA (2006)
A Parker-Forney-Traub like algorithm for quasiseparable-Hessenberg-Vandermonde matrices (with V. Olshevsky), Minisymposium on Structured Matrices, IWOTA 2005 - Storrs, CT, USA (2005)
Refereed Talks
The Equivalence of Pseudo-noise and Hadamard-Sylvester matrices (with V. Olshevsky, L. Sakhnovich), SPIE 2005 - San Diego, CA (2005)
Quasiseparable matrices and polynomials (with V. Olshevsky), Hans Schneider 80th Birthday Meeting, UConn, Storrs, CT (2007)
The Equivalence of Pseudo-noise and Hadamard-Sylvester matrices (with V. Olshevsky, L. Sakhnovich), ILAS 2005 - Regina, Canada (2005)
The generalized Bjorck-Pereyra algorithm for Szego-Vandermonde matrices based on properties of unitary Hessenberg matrices (with V. Olshevsky, I. Gohberg, I. Koltracht, Y. Eidelman), ILAS 2005 - Regina, Canada (2005)
Introduction to Linear Codes, Series in Linear Codes, SIGMA Seminar, University of Connecticut (2004)
The Equivalence of Pseudo-noise and Hadamard-Sylvester matrices (with V. Olshevsky, L. Sakhnovich), ILAS 2004 - Coimbra, Portugal (2004)
