UCSB Engineering

Shivkumar Chandrasekaran

Associate Professor

Contacts

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

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

Research Description

His current research interests include the development of new stable algorithms for the fast updating and downloading of structured systems of linear equations, the development of highly accurate and efficient algorithms for the numerical solution of differential and integral equations, and the development of new accurate and efficient algorithms for inverse scattering and computer vision problems.

Biography

Shiv's Ph.D. thesis involved the design of provably accurate and efficient algorithms for various problems in numerical linear algebra. He classified all then known algorithms for the rank-revealing QR decomposition and showed why they were likely to fail. He then developed the first accurate algorithms to compute this decomposition which would also be efficient in practice. He proposed a new parallelizable variant of the QR algorithm for computing the singular value decomposition. He then developed a provably accurate and efficient version of inverse iteration for computing the eigenvectors of hermitian matrices. This was done after he discovered that existing implementations could fail drastically. He also studied the perturbation behavior of linear and least-squares systems, and eigenvalue and singular value decompositions. This led to the development of sharp perturbation bounds for the components of linear systems. After defending his thesis Shiv worked for a year as a Visiting Instructor at the Mathematics Department of North Carolina State University in Raleigh. At UCSB he developed the first efficient and stable algorithm for the symmetric-definite generalized eigenvalue problem. In collaboration with Prof. Ali H. Sayed (UCLA) he developed the first unconditionally backward stable, fast algorithm for solving nonsymmetric Toeplitz and quasi-Toeplitz systems of linear equations. They also stabilized the fast Schur algorithm for factorizing matrices with displacement structure. In joint work with Prof. Sayed and Prof. Ming Gu (UCLA) they developed the first efficient and stable algorithms for the indefinite least-squares problem and for the diagonally weighted recursive least-squares problem. Also collaborating with Prof. Gene Golub (Stanford University) they developed an efficient algorithm for a new bounded errors-in-variables model of parameter estimation

Awards/Honors

• Recipient, B.I.T.S Merit Scholarship