
Conference on Experimental and Constructive Mathematics (CECM) 99  Analysis Day
(Wednesday) August 4, 1999Room K9509, Burnaby Campus, Simon Fraser University
Schedule of Talks 
9:00  9:45 
Heinz Bauschke, Okanagan University College
Accelerating the Convergence of the Method of Alternating Projections
The powerful von NeumannHalperin method of alternating projections (MAP) is an algorithm for determining the best approximation to any given point in a Hilbert space from the intersection of a finite number of subspaces.
In this talk, I consider an accelerated version of this algorithm originally suggested (but not analyzed) by GubinPolyakRaik. I explain when and why this method really accelerates.
(Based on joint work with Frank Deutsch, Hein Hundal, and SungHo Park.)

9:45  10:30 
Adrian Lewis, University of Waterloo
Illconditioned Systems of Inequalities
Convex processes provide an elegant tool for studying both cones and inequality systems. I will show that the smallest linear perturbation making a convex process nonsurjective has norm the reciprocal of the norm of the inverse process. This generalizes the fundamental property of the condition number of a linear map. I will then apply this result to strengthen a theorem of Renegar measuring the size of perturbation necessary to make an inequality system inconsistent. This measure is fundamental in the complexity of corresponding interior point methods.

10:30  10:45 
Coffee Break 
10:45  11:30 
Ivaylo Kortezov, Simon Fraser University
Game Approach and Fragmentability Properties of Function Spaces
Using some theorems of P. Kenderov and W. Moors for characterizing fragmentability and sigmafragmentability of topological (in particular Banach) spaces, we prove fragmentability of certain classes of function spaces and show some preservation results under topological operations.

11:30  12:15 
Joel Kamnitzer, University of Waterloo
Central Binomial Sums
The following interesting summations are well known: \sum _{n=0}^\infty \frac{1}{2n choose n}{n^2} = \Zeta(2)/3 and
\sum _{n=0}^\infty \frac{(1)^{n+1}}{2n choose n}{n^3} = \frac{2}{5} \Zeta(3)
with the latter playing a key roal in Apery's proof that \Zeta(3) is irrational.
Our goal is to extend these results by expressing the sum S(k) = \sum _{n=0}^\infty \frac{1}{2n choose n}{n^k} in terms of Zeta values. Along the way we are lead to Multiple Claussen Values, which prove to be an interesting area of study in their own right.

12:15  1:30 
Lunch Break 
1:30  3:30 
Xianfu Wang, Simon Fraser University
Fine and Pathological Properties of Subdifferentials (Thesis Defence)
Please note: Thesis defence takes place in Room AQ4100. 
3:30  4:15 
Roland Girgensohn, National Research Center for Environment and Health, Institute of Biomathematics and Biometry, Neuherberg, Germany.
Schauder Bases Consisting of Orthogonal Polynomials
We construct Schauder bases for the space $C[1,1]$ which consist of algebraic polynomials orthogonal with respect to a given weight function (e.g., Jacobi weights). The polynomials are of minimal degree, that is, for given $\varepsilon>0$ there is such a basis~$\{p_\mu\}_{\mu=0}^\infty$ with $\deg p_\mu \le (1+\varepsilon)\,\mu$ for all $\mu \in I\!\!N_0$.
When constructing orthogonal Schauder bases, one has to estimate certain Lebesgue constants. Here we use ideas from wavelet theory for this purpose. The space $C[1,1]$ is decomposed into a sequence of finitedimensional subspaces, consisting of polynomials and orthogonal
to each other, which can be thought of as spaces of wavelets: each space is the span of (generalized) translates of a certain generating polynomial. In this way, the estimation of Lebesgue constants can be reduced to estimates for these finitedimensional subspaces.

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