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Department of Mathematics

On a Conjecture of C. Sundberg: A Numerical Investigation

Prof. Roland Glowinski

Cullen Professor of Mathematics, University of Houston
Member of the French National Academy of Sciences
Member of the Academia Europaea
Member of the French National Academy of Technology
Seymour Cray Prize-France (1988)
Grand Prix Marcel Dassault (1996)
SIAM Theodore Von Karman Prize (2004)


Date: 24 May 2011 (Tuesday)

4:15 - 5:15 pm (Preceded by Reception at 3:45 pm)


FSC1217, Fong Shu Chuen Building,
Ho Sin Hang Campus, Hong Kong Baptist University



Carl Sundberg from University of Tennessee-Knoxville conjectured that


Our goal is to use a computational approach to investigate if (CSI) holds and to compute the related supremum, assuming it is finite. To do so, we observe that the supremum in (CSI) is equal to:



The strategy we advocate at the moment is a pretty crude one, namely, tabulate the function in order to get information on the boundedness of the supremum in (CSI). In our lecture, we will discuss the numerical computation of F(alpha), the associated problem of Calculus of Variations being solved by a methodology combining a finite difference discretization and an augmented Lagrangian algorithm associated with the following three families of linear constraints v-q_0=0, v'-q_1 =0 and v''-q_2 = 0.

The results of numerical experiments (with a in the range [0,10^6]) will be presented; we will discuss the conclusions we can draw from them concerning the veracity of (CSI).




All are welcome