[FRIAM] Looking for an algorithm

[Jon Zingale]

"There are some references to using tensor products to solve potential
equations that go back to 1964. They involve inverting (division?) of a
tensor product matrix. I had some of this in my thesis (1968) and is also
on the book I wrote that came our around 1972. I only have one copy left
(its pages are turning yellow with age). I can scan those pages if you
like."

I suspect you and I are talking past each other. I am not talking about
inverting a matrix, and I am not sure you are following the problem. I can
only guess that you are responding to my prompt:

"It is surprising that it took until the 90s for the problem to bite
someone and for explicit algorithms to emerge."

In case you are coming late to the thread, I am referring to factoring a
square matrice M into pairs of square matrices (P, Q) such that P⊗Q = M. Is
this what you are talking about? It appears that this problem, known as
NKP, has only recently been considered. Maybe I'm wrong?

To some extent, I am experiencing this thread like:

[setting Egypt, 300 BC]

Researcher: Hmm, does anyone know of an algorithm for finding whether or
not a given number divides another given number?

The Chorus: In Alexandria, a great number of people have put work into the
problem, some use blocks and others pitchers of water.

Researcher: Huh, it seems here, after consulting a colleague that a certain
Euclid has found such an algorithm. It surprises me that for as long as we
have had multiplication it is only recently that one of us has found a way
to factor.

Academic: Well, in my work, predating Euclid, I multiplied many numbers.
What say you?

Is this what we are doing?
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