We present new algorithms for computing the values of the Schur
s
λ
(
x
1
,
x
2
,
…
,
x
n
)
s_\lambda (x_1,x_2,\ldots ,x_n)
and Jack
J
λ
α
(
x
1
,
x
2
,
…
,
x
n
)
J_\lambda ^\alpha (x_1,x_2,\ldots ,x_n)
functions in floating point arithmetic. These algorithms deliver guaranteed high relative accuracy for positive data (
x
i
,
α
>
0
x_i, \alpha >0
) and run in time that is only linear in
n
n
.