<s>
The	O
Kantorovich	B-Algorithm
theorem	I-Algorithm
,	O
or	O
Newton	O
–	O
Kantorovich	B-Algorithm
theorem	I-Algorithm
,	O
is	O
a	O
mathematical	O
statement	O
on	O
the	O
semi-local	O
convergence	B-Algorithm
of	O
Newton	O
's	O
method	O
.	O
</s>
<s>
The	O
Kantorovich	B-Algorithm
theorem	I-Algorithm
gives	O
conditions	O
on	O
the	O
initial	O
point	O
of	O
this	O
sequence	O
.	O
</s>
<s>
the	O
Newton	O
iteration	O
starting	O
in	O
converges	O
to	O
with	O
at	O
least	O
linear	O
order	O
of	O
convergence	B-Algorithm
.	O
</s>
<s>
In	O
1986	O
,	O
Yamamoto	O
proved	O
that	O
the	O
error	O
evaluations	O
of	O
the	O
Newton	O
method	O
such	O
as	O
Doring	O
(	O
1969	O
)	O
,	O
Ostrowski	O
(	O
1971	O
,	O
1973	O
)	O
,	O
Gragg-Tapia	O
(	O
1974	O
)	O
,	O
Potra-Ptak	O
(	O
1980	O
)	O
,	O
Miel	O
(	O
1981	O
)	O
,	O
Potra	O
(	O
1984	O
)	O
,	O
can	O
be	O
derived	O
from	O
the	O
Kantorovich	B-Algorithm
theorem	I-Algorithm
.	O
</s>
<s>
There	O
is	O
a	O
q-analog	O
for	O
the	O
Kantorovich	B-Algorithm
theorem	I-Algorithm
.	O
</s>
<s>
Oishi	O
and	O
Tanabe	O
claimed	O
that	O
the	O
Kantorovich	B-Algorithm
theorem	I-Algorithm
can	O
be	O
applied	O
to	O
obtain	O
reliable	O
solutions	O
of	O
linear	B-Algorithm
programming	I-Algorithm
.	O
</s>
