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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This webpage is no longer maintained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 online:

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) 79120.

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) 369392.

S. Mitchell
and S. Vavasis, ``An aspect ratio bound for triangulating a dgrid
cut by a hyperplane''
(compressed
postscript, 118k;
plain
postscript, 339k). Extended abstract appeared in Proc. 1996
Symp. Comput. Geom., ACM Press, 4857.
 T.
Driscoll and S. Vavasis,
``Numerical conformal mapping using crossratios and Delaunay triangulation''
(gzip'd postscript, 139k;
plain
postscript, 395k).
Final version appeared in
SIAM J. Sci. Comp. 19 (1998) 17831803.

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) 13341370.

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) 11531174.

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) 6975.

V. Howle
and S. Vavasis,
``Preconditioning complexsymmetric 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) 400414.

V. Howle and S.
Vavasis, ``An iterative method for solving complexsymmetric systems arising
in electric power modeling''
(gzip'd
postscript, 123k;
plain
postscript, 343k). Final version appeared:
SIAM J. Matrix Analysis App.,
26 (2005) 11501178

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) 221262

S. Vavasis, ``A BernsteinBezier 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) 679701, 2003.

P. Ganguly, S. Vavasis and K.
Papoulia,
``An algorithm for twodimensional mesh generation based on the
pinwheel tiling''
(pdf,
289k)

E. Boman,
B. Hendrickson,
and S. Vavasis,
``Solving Elliptic Finite Element Systems in NearLinear 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 pinwheelbased mesh, submitted
to International J. Numer. Meth. Eng.
(pdf, 291k)

ChinHang 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 PrimalDual InteriorPoint 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 opensource 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 sourcecode 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 online documentation.
