Re: [Algorithms] decompose onto non-orthogonal vectors

[Peter D. <pd...@mm...>]

> And further, it appears to me that if you don't already know that p is
> a linear combination of a and b, then the Gaussian elimination
> solution is somewhat shorter than your algorithm above.

To further beat this dead horse:

Yes, a coordinate-based solution may indeed be shorter algorithmically. The
method I presented wasn't meant to be the most efficient one. I wanted to
give the OP (Ben?) an idea how to proceed in situations like this.

When you have one vector equation with several scalar unknowns, as in this
case, the trick is to project the equation along several (linearly
independent) axes and solve the resulting linear system.

The axes usually chosen are the coordinate axes - this corresponds to
dotting the equation with the basis vectors.

This problem demonstrated a situation where a different set of axes proves
to be useful for the projection, namely the a and b vectors.

--
Peter Dimov
Multi Media Ltd.