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 integer n, a property of the polynomial of degree n, which is the best possible approximation to ƒ(x) in the sense that the maximum absolute value of en (x) = ƒ(x) -pn (x) is as small as possible; namely, that en (x) assumes its extreme values at least n + 2 times, with the consecutive extrema having opposite signs.