Numerical work of Hans F. Weinberger

Saturday, October 4, 2008 - 2:00pm - 2:50pm
EE/CS 3-180
John Osborn (University of Maryland)
In this talk we will survey several papers (listed
below) by
Hans Weinberger dealing with numerical and approximation
issues. We have
divided them into three categories: (i) approximation of
eigenvalues; (ii)
approximation theory issues; and (iii) error bounds for
iterative methods for
matrix inversion.

The seven papers listed are only a small part of Hans’ work—but
were very influential. We, of course, cannot discuss any of
these papers
in detail, but will instead concentrate on those results that
are especially
insightful and elegant.


Approximation of Eigenvalues

[1] Upper and lower bounds for eigenvalues by finite difference
Communications on Pure and Appl. Math. 9 (1956), pp. 613-623.

[2] Lower bounds for higher eigenvalues by finite difference
methods. Pacific
J. Math. 8 (1958), pp. 339-368.

Approximation Theory Issues

[3] Optimal approximations and error bounds (joint with M.
Golumb). In
Proc. Symposium on Numerical Approximation, Univ. of Wisconsin
Press, 1959, pp. 117-190.

[4] Optimal approximation for functions prescribed at equally
spaced points.
Nat. Bureau of Standards J. of Research 65B, 2 (1961), pp.

[5] On optimal numerical solution of partial differential
equations. SIAM J.
Numer. Anal. 9 (1972), pp. 182-198.

[6] Optimal numerical approximation of a linear operator.
Linear Alg. and
its Appl. 52/53 (1983), pp. 717-737.

Error Bounds for Iterative Methods for Matrix Inversion

[7] A posteriori error bounds in iterative matrix inversion. In
Treatment of Partial Differential Equations, Academic Press
pp. 153-163. Proceedings of Symposium on Numerical Solution of
Differential Equations, held at the Univ. of Maryland in 1965
(Edited by
J. Bramble).