<s>
Sinc	B-Algorithm
approximation	O
methods	O
excel	O
for	O
problems	O
whose	O
solutions	O
may	O
have	O
singularities	O
,	O
or	O
infinite	O
domains	O
,	O
or	O
boundary	O
layers	O
.	O
</s>
<s>
The	O
truncated	O
Sinc	B-Algorithm
expansion	O
of	O
f	O
is	O
defined	O
by	O
the	O
following	O
series	O
:	O
</s>
<s>
approximation	O
of	O
derivatives	B-Algorithm
,	O
</s>
<s>
approximation	O
and	O
inversion	O
of	O
Fourier	B-Algorithm
and	O
Laplace	O
transforms	O
,	O
</s>
<s>
approximation	O
of	O
Hilbert	B-Algorithm
transforms	I-Algorithm
,	O
</s>
<s>
approximation	O
of	O
definite	O
and	O
indefinite	O
convolution	B-Language
,	O
</s>
<s>
approximate	O
solution	O
of	O
integral	B-Algorithm
equations	I-Algorithm
,	O
</s>
<s>
In	O
the	O
standard	O
setup	O
of	O
the	O
sinc	B-Algorithm
numerical	I-Algorithm
methods	I-Algorithm
,	O
the	O
errors	O
(	O
in	O
big	O
O	O
notation	O
)	O
are	O
known	O
to	O
be	O
with	O
some	O
c>0	O
,	O
where	O
n	O
is	O
the	O
number	O
of	O
nodes	O
or	O
bases	O
used	O
in	O
the	O
methods	O
.	O
</s>
<s>
However	O
,	O
Sugihara	O
has	O
recently	O
found	O
that	O
the	O
errors	O
in	O
the	O
Sinc	B-Algorithm
numerical	I-Algorithm
methods	I-Algorithm
based	O
on	O
double	O
exponential	O
transformation	O
are	O
with	O
some	O
k>0	O
,	O
in	O
a	O
setup	O
that	O
is	O
also	O
meaningful	O
both	O
theoretically	O
and	O
practically	O
and	O
are	O
found	O
to	O
be	O
best	O
possible	O
in	O
a	O
certain	O
mathematical	O
sense	O
.	O
</s>
