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A comment on The End of Numeric Error: An interview with John L. Gustafson. Parent comment

Re:The End of Numeric Error: An interview with John L. Gusta... by bsder on Tuesday April 26, 2016 @04:17PM (#11575259)
"vast majority"? Maybe.

But anything which uses matrices (aka. systems of linear differential equations), always runs into some pathological cases. Quite often, they aren't even uncommon.

Systems which have vastly different time constants in the same system are ALWAYS a problem. Simulating RF circuits or phase locked loops is always an issue.

Computational fluid dynamics always has boundary conditions that challenge infinity/zero and drive the solver crazy.

Something as pedestrian as simulating basic cotton cloth accurately is problematic (the warp/weft redistributes energy on a much faster time scale than gravity pulls the cloth down).

A lot of people did a lot of research and put in a lot of programming hours to make solving these problems relatively easy without understanding the gory details.

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Re:The End of Numeric Error: An interview with John L. Gusta... by zevets on Tuesday April 26, 2016 @09:11PM (#11577125)
But will unums help? No matter how an ill conditioned matrix is represented, it will still be ill conditioned, and we'll still be iterating, unless I've missed something in this article.

I'm skeptical that changing how we represent the numbers will help - when the physics are icky, they're icky.

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Re:The End of Numeric Error: An interview with John L. Gusta... by tjl on Tuesday April 26, 2016 @09:27PM (#11577200)
It won't really help. You'll get the same issues with stiff DEs or ill-conditioned matrices for perfect precision or floating-point. There will be some cases where it will help, but not a lot.

I've implemented a few DE solvers and sparse matrix implementations before. I think sparse matrices is one case where it would help.

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Re:The End of Numeric Error: An interview with John L. Gusta... by tanderson92 on Tuesday April 26, 2016 @09:25PM (#11577192)
Yes, this won't change the challenging nature of solving the underlying problem.

More problematic is that when a matrix is ill-conditioned it may not be all that helpful to have "an answer" since the ill-conditioning tells you there are many solutions closely satisfying the system of equations.

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