Numerical Linear Algebra
where the algebra stops being the arithmetic
Ladder

Cancellation — 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. 10⁻¹²10⁻¹⁰10⁻⁸10⁻⁶10⁻⁴10⁻²110⁻¹⁷10⁻¹⁴10⁻¹¹10⁻⁸10⁻⁵10⁻²10¹xrelative error of the computed value(1 − cos x)/x², as written2 sin²(x/2)/x²no digits left at alldouble precision throughoutone function, two spellings

    Cancellation takes the answer, not a digit

    Subtracting two nearly equal numbers is exact. That is what makes it dangerous — the subtraction introduces no error at all, it exposes error the operands were already carrying, and the exposure can consume every significant figure at once.

    rung 1 · arithmetic

All ladders