Disk drive iteratively adapting correction value that compensates for non-linearity of head

A disk drive is disclosed comprising a head actuated over a disk. A position y of the head is measured based on servo sectors, and the measured position y of the head is adjusted based on: z1=y+c1(y) where z1 represents a first adjusted position and c1(y) represents first correction values. The first adjusted position z1 is adjusted based on: z2=z1+c2(z1) where z2 represents a second adjusted position and c2(z1) represents second correction values. The first and second correction values are combined based on: c3(y)=c1(y)+c2(y+c1(y)). The measured position y of the head is adjusted based on: z3=y+c3(y) where z3 represents a third adjusted position comprising the adjustment based on c1(y) and the adjustment based on c2(y), and c3(y) represents third correction values.