<s>
In	O
mathematics	O
,	O
moduli	B-Algorithm
of	I-Algorithm
smoothness	I-Algorithm
are	O
used	O
to	O
quantitatively	O
measure	O
smoothness	O
of	O
functions	O
.	O
</s>
<s>
Moduli	B-Algorithm
of	I-Algorithm
smoothness	I-Algorithm
generalise	O
modulus	O
of	O
continuity	O
and	O
are	O
used	O
in	O
approximation	B-Algorithm
theory	I-Algorithm
and	O
numerical	B-General_Concept
analysis	I-General_Concept
to	O
estimate	O
errors	O
of	O
approximation	O
by	O
polynomials	O
and	O
splines	B-Algorithm
.	O
</s>
<s>
Moduli	B-Algorithm
of	I-Algorithm
smoothness	I-Algorithm
can	O
be	O
used	O
to	O
prove	O
estimates	O
on	O
the	O
error	O
of	O
approximation	O
.	O
</s>
<s>
Due	O
to	O
property	O
(	O
6	O
)	O
,	O
moduli	B-Algorithm
of	I-Algorithm
smoothness	I-Algorithm
provide	O
more	O
general	O
estimates	O
than	O
the	O
estimates	O
in	O
terms	O
of	O
derivatives	O
.	O
</s>
<s>
For	O
example	O
,	O
moduli	B-Algorithm
of	I-Algorithm
smoothness	I-Algorithm
are	O
used	O
in	O
Whitney	B-Algorithm
inequality	I-Algorithm
to	O
estimate	O
the	O
error	O
of	O
local	O
polynomial	O
approximation	O
.	O
</s>
