Greedy algorithm — where it appears
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
The points the algorithm chose
A rational approximant whose support points are picked by its own residual clusters geometrically at a branch point nobody named — recovering by measurement the rule a hand-built approximant is given. At degree ten it is seven hundred and fifty times more accurate than the same form with its points spread evenly.
What reading the next pivot buys
In a fraction-free elimination every pivot is paid for twice — it multiplies every entry of its own step and divides every entry of the next — and the rule that picks the smallest pivot entry left a median 20 per cent above the least arithmetic any row order reaches. A rule that charges two steps ahead brings the median matrix to within 2.5 per cent, and on one matrix of twenty-four costs 1.87 times the least, worse than the smallest pivot ever does. Charging three steps ahead finds the least of all 40,320 orders on thirteen matrices and is never more than 27 per cent above it. And none of it pays: choosing that way costs forty to two hundred and sixty times the elimination it chooses.
Named alongside it
The objects these essays reach for when they reach for this one.
Adaptive interpolationApproximation before linearisationBarycentric formBit lengthBranch pointData-driven realisationDeterminantExact arithmeticExact ground truthFraction-free eliminationLoewner matrixMinor