A correction fraction of one half moves halfway to the target each step. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Half correction moves halfway to the target

Starting at 0 volts with target 8 volts, correction 1/2 moves to 4 volts.

0+12(8(0))=40+{1\over 2}(8-(0))=4
Half correctionEvery sampled state and error is checked.s0e0s1e1s2e2s3e3

The remaining error halves each step

The checked states are 0, 4, 6, 7 volts, with final error 1 volt.

0,4,6,7e=1 V0,4,6,7\quad e=1\ \text{V}
Damped approachThe error bars shrink with the same checked rule.s0e0s1e1s2e2s3e3