Numerical Linear Algebra
where the algebra stops being the arithmetic
Ladder

Summation — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. 10¹10²10³10⁴10⁵10⁶10⁻⁹10⁻⁷10⁻⁵10⁻³10⁻¹number of terms addedrelative error against the exact sumin orderin a treecompensatedbinary32 · terms are 1/icompensated: 3·10⁻⁸

    The order they are added in

    Addition is associative in the algebra and is not associative in the arithmetic. The same million numbers, added in a different order, give answers that differ in the third significant figure — and the fix is not a wider float, it is a different order.

    rung 2 · arithmetic

All ladders