Seymour V. Parter

Professor of Computer Sciences and Mathematics

Computer Sciences Department
University of Wisconsin
1210 W. Dayton St.
Madison, WI 53706-1685

telephone: (608) 262-1204
fax: (608) 262-9777
Ph.D., New York University, 1958
Interests: Numerical methods for partial differential equations

Research Summary

At this time the major emphasis of my work is on the solution of indefinite, discrete elliptic systems of equations. Classical iterative methods and most multigrid methods only work effectively when the system is positive definite. These methods can also be made effective when the real or symmetric part of the operator is positive definite. On the other hand, in the indefinite case direct methods which attempt to preserve the `sparseness' of the system may encounter (very) small `pivots.' Thus, this is a challenging problem which effectively mixes concepts and procedures from linear algebra and elliptic partial differential equations. I am now involved in several projects which attack this class of problems. These include preconditioning studies and research on special multigrid methods.

Sample Recent Publications

Preconditioning Chebyshev collaction discretization for elliptic partial differential equations, to appear in SIAM Journal on Numerical Analysis.

Preconditioning and boundary conditions without H(2) estimates: L(2) condition numbers and the distribution of the singular values, SIAM Journal on Numerical Analysis, vol. 30, pp. 343-376, 1993.

Preconditioning second-order elliptic operators: Condition numbers and the distribution of the singular values, Journal of Scientific Computing, vol. 6, pp. 129-157, 1991.

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