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Conference on Experimental and Constructive Mathematics (CECM) 99 -- Analysis Day
(Wednesday) August 4, 1999--Room 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 Neumann-Halperin 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 Gubin-Polyak-Raik. I explain when and why this method really accelerates.
(Based on joint work with Frank Deutsch, Hein Hundal, and Sung-Ho Park.)
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9:45 - 10:30 |
Adrian Lewis, University of Waterloo
Ill-conditioned 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.
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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 sigma-fragmentability of topological (in particular Banach) spaces, we prove fragmentability of certain classes of function spaces and show some preservation results under topological operations.
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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.
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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 finite-dimensional 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 finite-dimensional subspaces.
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Go to CECM 99.
Go to MITACS Day Schedule.
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