"exponentially ill-posed"

[fflo]

Kind of a harsh-sounding term, don't you think? Context:

The authors consider an inverse heat conduction problem in a quarter
plane. The goal of the specific inverse problem is to determine the
surface heat flux in a body from a measured temperature history at a
fixed location inside the body. The standard example is the sideways
heat equation. This type of inverse problem is known to be
exponentially ill-posed.

Fortunately,

The authors propose a Fourier regularization method and prove order
optimal logarithmic stability estimates. A simple numerical example is
presented to verify the analytical results.

Phew!

ha ha ha

Comments

[vjsmom.livejournal.com]

The authors propose a Fourier regularization method and prove order
optimal logarithmic stability estimates. A simple numerical example is
presented to verify the analytical results.

Exactly what I was going suggest that they do!

[fflo.livejournal.com]

It really is the obvious solution, once you think about it.

Scary Flashbacks!

[peteralway.livejournal.com]

Most esoteric math talk drips off me like water off a duck's back. But I remember that once I was humiliated by my inability to calculate surface heat flux in a solidy body. Back when I was a lad and didn't have the sense to find the help I needed. So this post is haunting me with unfinished busininess flashbacks. I have to remind myself that there is no need for me to learn to numerically calculate the temperature gradient needed to maintain a symmetrical layer of liquid deuterium-tritium inside a glass shell. That job is over, and the company defunct.

Exponentially Ill-posed indeed!

[queerbychoice.livejournal.com]

It's always nice to be reminded that there are even worse things I could be assigned to edit than what I actually have been assigned to edit. Databases and strings of numbers are awfully boring for me to edit, but at least I know what they mean.