Stephen A. Vavasis

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Cornell

Some External activities

Professor (PhD, Stanford, 1989)
Department of Computer Science
493 Rhodes Hall (Mailing address: 4130 Upson Hall)
Cornell University
Ithaca, NY 14853

Steve Vavasis moved to University of Waterloo on Sep. 1, 2006. This webpage is no longer maintained

email: vavasis@cs.cornell.edu

Vavasis's CV (last updated 8/19/05)

Courses

In the fall of 2005, I taught CS421, Numerical Analysis.

In the spring of 2006, I am teaching

Research and Publications

My research interest is numerical analysis. (You aren't sure what numerical analysis is? Please see the essay by L. N. Trefethen.) More specifically, I am interested in:

Numerical optimization and complexity issues
Numerical methods for boundary value problems
Geometric problems arising in scientific computing
Numerical linear algebra

I have a few recent manuscripts available on-line:

S. Vavasis and Y. Ye, ``A primal dual accelerated interior point method whose running time depends only on A'' (compressed postscript, 170k). Final version appeared in Math. Progr. 74 (1996) 79-120.
P. Hough and S. Vavasis, ``Complete orthogonal decomposition for weighted least squares'' (gzip'd postscript, 84k; plain postscript, 330k). Final version appeared in SIAM J. Matrix Anal. Appl., 18 (1997) 369-392.
S. Mitchell and S. Vavasis, ``An aspect ratio bound for triangulating a d-grid cut by a hyperplane'' (compressed postscript, 118k; plain postscript, 339k). Extended abstract appeared in Proc. 1996 Symp. Comput. Geom., ACM Press, 48-57.
T. Driscoll and S. Vavasis, ``Numerical conformal mapping using cross-ratios and Delaunay triangulation'' (gzip'd postscript, 139k; plain postscript, 395k). Final version appeared in SIAM J. Sci. Comp. 19 (1998) 1783-1803.
S. Mitchell and S. Vavasis, ``Quality Mesh Generation in Higher Dimensions'' (gzip'd postscript, 130k; plain postscript, 388k). Final version appeared in SIAM J. Comput. 29 (2000) 1334-1370.
E. Bobrovnikova and S. Vavasis, ``Accurate Solution of Weighted Least Squares by Iterative Methods'' (gzip'd postscript, 105k; plain postscript, 349k). Final version appeared SIAM J. Matrix An. App 22 (2001) 1153-1174.
E. Bobrovnikova and S. Vavasis, ``A Norm Bound for Projections with Complex Weights'' (gzip'd postscript, 106k; plain postscript, 215k). Final version appeared Linear Alg. Appl. 307 (2000) 69-75.
V. Howle and S. Vavasis, ``Preconditioning complex-symmetric layered systems arising in electric power modeling'' (gzip'd postscript, 42k; plain postscript, 156k).
S. Vavasis, ``A note on efficient computation of the gradient in semidefinite programming'' (gzip'd postscript, 99k; plain postscript, 196k).
G. Jónsson and S. Vavasis, ``Solving polynomials with small leading coefficients'' (gzip'd postscript, 100k; plain postscript, 290k). Final version appeared: SIAM J. Matrix Analysis App., 26 (2005) 400-414.
V. Howle and S. Vavasis, ``An iterative method for solving complex-symmetric systems arising in electric power modeling'' (gzip'd postscript, 123k; plain postscript, 343k). Final version appeared: SIAM J. Matrix Analysis App., 26 (2005) 1150-1178
G. Jónsson and S. Vavasis, ``Accurate solution of polynomial equations using Macaulay resultant matrices'' (gzip'd postscript, 284k; plain postscript, 689k). Final version appeared: Mathematics of Computation, 74 (2005) 221-262
S. Vavasis, ``A Bernstein-Bezier sufficient condition for invertibility of polynomial mapping functions'' (revised 3 Nov 2001) (gzip'd postscript, 100k; plain postscript, 200k).
K. Papoulia and S. Vavasis, ``Time continuity in cohesive finite element modeling'' (pdf, 319k). Final version appeared: International Journal for Numerical Methods in Engineering 58(5) 679-701, 2003.
P. Ganguly, S. Vavasis and K. Papoulia, ``An algorithm for two-dimensional mesh generation based on the pinwheel tiling'' (pdf, 289k)
E. Boman, B. Hendrickson, and S. Vavasis, ``Solving Elliptic Finite Element Systems in Near-Linear Time with Support Preconditioners'' (pdf, 181k)
K. Papoulia, S. Vavasis and P. Ganguly, Spatial convergence of crack nucleation using a cohesive finite element model on a pinwheel-based mesh, submitted to International J. Numer. Meth. Eng. (pdf, 291k)
Chin-Hang Sam, K. Papoulia, Stephen Vavasis, Obtaining initially rigid cohesive finite element models that are temporally convergent, to appear, Engineering Fracture Mechanics, (pdf, 310k)
S. Shontz and S. Vavasis, ``A linear weighted laplacian smoothing framework for warping tetrahedral meshes'' (arxiv link)
Gun Srijuntongsiri and S. Vavasis, A Fully Sparse Implementation of a Primal-Dual Interior-Point Potential Reduction Method for Semidefinite Programming, submitted to SIAM Journal on Optimization (arxiv link)
S. Vavasis, A conjecture that the roots of a univariate polynomial lie in a union of annuli, (arxiv link)

Applied Math

I am a member of the Center for Applied Mathematics at Cornell. This interdisciplinary center promotes applied math and is in charge of the Applied Math PhD program.

The QMG package

I have written a software package called QMG for mesh generation for the finite element method in three dimensions. QMG is available on an open-source basis by anonymous ftp. With QMG you can construct 3D geometric objects with very complicated topology (holes, internal boundaries, etc.) and automatically create an unstructured tetrahedral mesh for them. (The mesh generator is based on algorithmic work by Scott Mitchell and me.) You can also solve an elliptic boundary value problem (div (c*grad u)=f) on your domain. The package is written in C++ and Matlab and is distributed for free at the source-code level (anonymous ftp distribution began 5/5/95). It runs under Matlab and Tcl/Tk.

QMG 2.0 was released on 3 September 1999. The principal new feature in QMG 2.0 (compared to QMG 1.1) is its ability to handle curved boundaries.

Please see the on-line documentation.