NARC Tomorrow: 100 Digit Problems

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Brian DeSilva

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Jan 17, 2018, 9:01:57 PM1/17/18

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Hi everyone,

Tomorrow in NARC we will discuss solutions to two of the SIAM 100-digit problems.

I will cover problem 1, which asks one to compute the following integral

$\lim_{\epsilon\to0}\int^1_\epsilon x^{-1}\cos\left(x^{-1}\log x\right)\mathrm{d}x.$

Bobby will talk about problem 3:

The infinite matrix $A$ with entries $a_{11}=1,~a_{12}=1/2,~a_{21}=1/3,~a_{13}=1/4,~a_{22}=1/5,~a_{31}=1/6,\dots$ is a bounded operator on $\ell^2$ . What is $\|A\|$ ?

The goal is to compute the solution to each problem to within at least 10 digits of accuracy.

As usual, we will have snacks. Hope to see you there!

Best,

Brian

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