TripleGrid Calculus
Author: Han de Bruijn
Date: 2006 Nov / 2019 Aug
This document is meant as an extension to a previously published one, called
MultiGrid Calculus. Upon retrospective, DoubleGrid Calculus would
have been a better name for the latter. The reason being that "Multigrid" is
much of a reserved word within the world of Numerical Analysis. Therefore its
use in a pure mathematics context will likely give rise to confusion. (But
maybe that's just intended?) Anyway, quite unexpectedly, it has been discovered
that there exists another kind of Multigrid Calculus, which is distinct from
DoubleGrid. It also works with coarsening and refinement of grids,
but does not double or halve the intervals. Instead, it makes these intervals
larger or smaller, not with a factor two, but with a factor three. Ah,
and now you could think that the next step is a MultiGrid Calculus employing
a factor four or maybe five. But this is not so. The factor four being already
covered by a double doubling in the first place. Furthermore, it can be proved
that factors five or higher are not an option, except as a powers of 2 and 3 .
Thus all possibilities for MultiGrid are exhausted with DoubleGrid and
TripleGrid. By the way, the DoubleGrid document has been available all
the time as Multigrid Calculus.
- Elimination
- Quotient Calculus
- DoubleGrid Product
- TripleGrid Product
- Stationary Points
- Grid Refinement
- Via the Cubic
- TripleGrid Refinement
- Chebyshev and stuff
Disclaimers
Anything free comes without referee :-(
My English may be better than your Dutch.