UCSB Engineering

Shivkumar Chandrasekaran

Professor

Electrical & Computer Engineering

Shivkumar Chandrasekaran

Contacts

Department of Electrical and Computer Engineering
University of California, Santa Barbara
Santa Barbara, CA 93106-9560

tel: (805) 893-7542
fax: (805) 893-3262
shiv@ece.ucsb.edu

Research Description

His current research interests include the development of fast numerical algorithms for structured matrices. He is also interested in the development of new efficient and accurate higher-order schemes for the discretization and solution of differential and integral equations.

Research Groups

Biography

Shiv obtained his Ph.D. in numerical analysis at Yale University in 1994. After spending a year as a Visiting Instructor at the Mathematics department of North Carolina State University, Raleigh, he joined UCSB as an Assistant Professor. His early work included the development of first fast rank-revealing QR algorithm, and the first numerically stable inverse iteration algorithm for computing the eigendecomposition of symmetric matrices. Then, in joint work with Prof. Ali Sayed of UCLA, he developed the first numerically stable and fast algorithms for Toeplitz and other matrices with displacement structure. He also worked jointly with Professors Gu (UC Berkeley), Sayed and Golub (Stanford), in providing fast algorithms for finding globally optimal solutions to linear systems with bounded errors in the data. More recently, in joint work with Prof. Gu, Dewilde (TU Delft) and others, he has developed an entire family of fast numerical algorithms for matrices with HSS (Hierarchically Semi-Separable) structure. In collaboration with Prof. Mhaskar (Cal. State. Los Angeles), he developed the first numerically stable algorithm for constructing linear interpolatory polynomials that can work in arbitrary dimensions with arbitrary scattered data.

Selected Publications

  • A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations, SIAM Journal on Matrix Analysis and Applications, vol.19, (no.1), Jan. 1998, 107-39, S. Chandrasekaran and A. H. Sayed
  • On Rank-Revealing QR Factorisations, SIAM Journal on Matrix Analysis and Applications, vol. 15, no. 2, April 1994, 592-622, S. Chandrasekaran and I. Ipsen
  • On the Numerical Rank of the Off-Diagonal Blocks of Schur Complements of Discretized Elliptic PDEs, SIAM Journal on Matrix Analysis and Applications, Vol. 31, No. 5, 2010, S. Chandrasekaran, P. Dewilde, M. Gu and N. Somasunderam
  • A Fast Solver for HSS Representations via Sparse Matrices, SIAM Journal on Matrix Analysis and Applications, Volume 29, Number 1, 2006, 67--81, S. Chandrasekaran, P. Dewilde, M. Gu, W. Lyons and T. Pals
  • Some Fast Algorithms for Sequentially Semi-separable Representations, SIAM Journal on Matrix Analysis and Applications, Volume 27, Number 2, 2005, 341--364, S. Chandrasekaran, P. Dewilde, M. Gu, T. Pals, X. Sun, A.-J. van der Veen and D. White
  • The Degenerate Bounded Errors-in-variables Mode, SIAM Journal on Matrix Analysis and Applications, Volume 23, Number 1, 138-166, S. Chandrasekaran, M. Gu, A. H. Sayed and K. E. Schubert