equal ripple property

equal ripple property [¦ē·kwəl ′rip·əl ‚präp·ərd·ē]

(mathematics)

For any continuous function ƒ(x) on the interval -1,1, and for any positive integern,a property of the polynomial of degreen, which is the best possible approximation to ƒ(x) in the sense that the maximum absolute value ofe_n(x) = ƒ(x) -p_n(x) is as small as possible; namely, thate_n(x) assumes its extreme values at leastn+ 2 times, with the consecutive extrema having opposite signs.