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[Phys-l] ill-posed problems



In the context of a Su Doku puzzle,
On 03/15/2010 07:07 AM, chuck britton wrote:

Does this in fact relate to the CT image generation?

Yes.

It also relates to seismology and a ton of other things.
All of these can be formulated as _deconvolution_ problems.

(JD's example below is four-fold degenerate?)

Yes. Constructed to be so.

=========

Why did I bring this up? Because we need more pedagogical
examples of ill-posed problems.

Real-world problems are usually ill-posed. For example,
in the classroom, when was the last time a student came
up to you and said "I'm confused, and here's exactly
what I'm confused about....." In any non-menial job,
the job description itself is ill-posed.

Outside the workplace, the situation is the same. The
question of what shoes to buy is ill-posed ... not to
mention the question of whom to vote for.

Yet in almost all the textbooks, the end-of-chapter
problems are all well-posed. There is precious little
discussion of
-- how to recognize problems that are overspecified
or underspecified
-- systematic procedures for dealing with such problems.

In this forum, the recent discussion of what happens
when you push on a gas with a piston went on for *days*
before John M. sorted out all the ways in which the
question was ill-posed.

I really like yesterday's load-sharing problem. It is
an easy-to-state 100% genuine problem. The physics is
easy, so it is easy to have a discussion of ill-posedness
without having to dig through any arcane physics to get
there.

The Su Doku problem doesn't require any physics at all,
but I had to tell a long story to connect it to real-world
applications.

It would be nice to have a collection of good pedagogical
examples of ill-posed problems. If anybody knows of such
a collection ... or who has a favorite example to share
... I'd very much appreciate hearing about it.