QnAs with Gilbert Strang

Piecewise Polynomials and the Finite Element Method by Gilbert Strang

Thirty years ago, Courant gave a remarkable lecture to this Society. My talk today is more or less a progress report on an idea which he described near the end of that lecture. There are a lot of people in this city, and a few in this room, who worked very closely with Courant—but the idea I am talking about came to fruition in a different and more unexpected way. To begin with, his idea was fo...

Toeplitz Operators in a Quarter-plane by Gilbert Strang

Explicit Relaxation of a Variational Problem in Optimal Design by Robert v. Kohn and Gilbert Strang

for vector-valued functions u on Lipschitz domains Q c R. The right side of (1) is the relaxation of the left, cf. [1]. Each infimum is over u G if(Q;R), lsupp Vu denotes the characteristic function of the support of Vu, and \Vu\ = E(<hi7cte*)The left side of (1) is a problem of optimal design: it minimizes Area(H \ S) + fQ \Vus\ 2 dx, among all sets S c O , where us solves the variational problem

TRIGONOMETRIC POLYNOMIALS AND DIFFERENCE METHODS OF MAXIMUM ACCURACY* By GILBERT STRANG

1. The fundamental problem in the theory of partial difference approximations to hyperbolic equations is the question of convergence to the true solution through the use of an increasingly fine mesh. We shall examine this question for those explicit methods of greatest interest, the most accurate ones. Happily, our answer is very different in kind from that given by Dahlquist [2] to a similar q...

QnAs with Angel Rubio.

Just as physics requires a different set of tools to explore phenomena at the quantum scale, chemistry requires a quantum paradigm. At the macroscale, the interaction of light with chemical entities can be observed in processes such as photosynthesis. But the actual interaction between photons and other matter occurs in the realm of quantum chemistry. National Academy of Sciences member and phy...