— Cleve ]]>

I met you at the Mathworks Summit in June, I spoke on the EHT, and we discussed Reuleaux triangle in the break. I am just getting round now to commenting, unfortunately comments are closed on the relevant blog post. The article which explains why the Reuleaux triangle is a useful configuration for a radio interferometer is this one, by my former colleague Eric Keto: https://iopscience.iop.org/article/10.1086/303545/pdf

and this notion was applied to set the dish positions for a telescope in Hawai’i called the Submillimeter Array: https://en.wikipedia.org/wiki/Submillimeter_Array

Sorry to put this in a wrong place. A pleasure to have met you.

Jonathan Weintroub ]]>

Interestingly, but this property cannot be verified in MATLAB when we use double precision [1] even for small n.

We must use extended precision because such innocent looking matrix has highly ill-conditioned eigenvalues.

Another interesting example is Circus matrix [2]. It is also Bohemian with nice looking plot of eigenvalues. But its eigenvalues are even more ill-conditioned. Maybe it worth adding to the gallery.

[1] https://www.advanpix.com/2011/10/12/multiprecision-computation-eigenvalues-eigenvectors/

[2] https://www.advanpix.com/documentation/users-manual/#Compute_sensitive_eigenvalues

I am wondering whether you could write on ill-conditioning in solving Ax=b, especially using iterative methods such as gradient descent method.

Thanks again.

Sangdon Lee ]]>