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n J
o
urna
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f
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lect
rica
l En
g
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nd
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m
pu
t
er
Science
Vo
l.
3
6
,
No
.
3
,
Dec
em
b
er
20
24
,
p
p
.
1
4
85
~
1
4
92
I
SS
N:
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502
-
4
7
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,
DOI
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1
1
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cs
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3
6
.
i
3
.
pp
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In
terp
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n
tec
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n
iq
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s
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a
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b
e
u
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d
to
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term
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a
p
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ter
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terp
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e
n
u
m
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rica
ll
y
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fra
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tal.
Th
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fra
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tal
in
t
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rp
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v
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is
in
fl
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d
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fa
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to
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d
th
e
fra
c
tal
in
t
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c
ti
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(F
IF
)
.
Th
is
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se
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h
in
tr
o
d
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c
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s
f
ra
c
tal
in
terp
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tec
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n
iq
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e
with
F
IF
wh
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is
c
o
n
str
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ted
fro
m
S
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p
in
sk
i
tr
ian
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a
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x
a
m
p
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o
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a
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p
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ti
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th
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ter
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lt
s
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term
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e
d
u
sin
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th
e
m
e
a
n
a
b
s
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p
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tag
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APE
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tri
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n
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3
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2
4
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th
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th
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n
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ica
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a
n
in
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re
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se
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th
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ter
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re
su
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ts
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d
th
a
t
th
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n
s
o
f
t
h
e
in
ter
p
o
lati
o
n
tec
h
n
iq
u
e
.
K
ey
w
o
r
d
s
:
Fra
ctal
I
n
ter
p
o
latio
n
I
n
v
en
to
r
y
Sier
p
in
s
k
i
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Fit
r
i M
ay
a
Pu
s
p
ita
Dep
ar
tm
en
t o
f
Ma
th
em
atics,
Un
iv
er
s
itas
Sriwijay
a
I
n
d
r
alay
a
,
Og
an
I
lir,
I
n
d
o
n
esi
a
E
m
ail: f
itrim
ay
ap
u
s
p
ita@
u
n
s
r
i.a
c.
id
1.
I
NT
RO
D
UCT
I
O
N
I
n
ter
p
o
latio
n
is
o
n
e
o
f
th
e
m
eth
o
d
s
f
o
r
d
eter
m
in
in
g
ap
p
r
o
x
im
ate
v
alu
es
with
k
n
o
wn
t
wo
in
ter
v
al
b
o
u
n
d
ar
y
v
al
u
es.
T
h
er
e
ar
e
two
in
ter
p
o
latio
n
tech
n
iq
u
e
s
,
n
am
ely
n
u
m
er
ical
in
ter
p
o
latio
n
an
d
f
r
ac
tals
in
ter
p
o
latio
n
.
T
h
e
ap
p
licatio
n
o
f
n
u
m
er
ical
in
ter
p
o
latio
n
te
ch
n
iq
u
es
h
as
b
ee
n
wid
ely
ca
r
r
ied
o
u
t
i
n
v
ar
io
u
s
f
ield
s
,
in
clu
d
in
g
th
e
f
in
a
n
cial
s
ec
to
r
[
1
]
.
E
s
tim
ate
an
d
p
r
ed
i
ct
th
e
g
as
co
n
ten
t
o
f
h
y
d
r
o
g
e
n
an
d
io
d
in
e
in
th
e
f
o
r
m
atio
n
o
f
io
d
ic
ac
id
r
ea
ctio
n
s
u
s
in
g
n
ewto
n
an
d
cu
b
ic
s
p
lin
es
in
ter
p
o
latio
n
m
e
th
o
d
[
2
]
.
Kr
i
g
in
g
in
ter
p
o
latio
n
with
n
o
n
lin
ea
r
f
u
n
ctio
n
s
is
em
p
lo
y
e
d
f
o
r
p
r
ed
ictin
g
r
o
ck
jo
in
t
s
h
ea
r
s
tr
en
g
th
[
3
]
,
wh
ile
th
e
co
-
k
r
ig
in
g
in
ter
p
o
latio
n
m
eth
o
d
is
u
tili
ze
d
f
o
r
m
u
lti
-
f
id
elity
an
aly
s
is
an
d
u
n
ce
r
tain
ty
q
u
a
n
tific
a
tio
n
o
f
b
ea
m
v
ib
r
atio
n
[
4
]
.
L
o
w
-
co
s
t
d
iv
e
altitu
d
e
s
en
s
o
r
in
r
em
o
tely
o
p
er
ated
u
n
d
e
r
wate
r
v
eh
icl
e
(
R
OV)
u
s
in
g
t
h
e
New
to
n
’
s
p
o
ly
n
o
m
ials
in
ter
p
o
latio
n
b
ased
-
er
r
o
r
co
r
r
ec
tio
n
m
eth
o
d
[
5
]
.
R
is
k
ev
alu
atio
n
o
f
in
v
estme
n
t
with
cu
b
ic
s
p
lin
e
in
ter
p
o
latio
n
[
6
]
.
A
l
ag
r
an
g
e
-
q
u
ad
r
atic
s
p
lin
e
o
p
tim
al
co
llo
ca
tio
n
m
et
h
o
d
f
o
r
th
e
tim
e
tem
p
er
e
d
f
r
ac
tio
n
al
d
if
f
u
s
io
n
eq
u
atio
n
[
7
]
.
L
ag
r
an
g
e
in
ter
p
o
latio
n
to
ad
ap
tiv
e
d
if
f
er
e
n
tial
ev
o
lu
tio
n
[
8
]
.
An
aly
s
is
o
f
ad
ap
tiv
e
d
ec
is
io
n
b
ased
in
v
e
r
s
e
d
is
tan
ce
weig
h
ted
in
ter
p
o
latio
n
(
DB
I
DW
I
)
alg
o
r
ith
m
f
o
r
s
alt
an
d
p
e
p
p
er
n
o
is
e
[
9
]
.
Dete
r
m
i
n
is
tic
in
ter
p
o
latio
n
m
eth
o
d
s
to
clim
ate
ch
an
g
e
d
etec
tio
n
in
Pen
an
g
I
s
lan
d
[
1
0
]
.
T
h
e
s
ec
o
n
d
in
ter
p
o
latio
n
tec
h
n
iq
u
e
is
f
r
ac
tal
in
ter
p
o
latio
n
.
T
h
e
a
p
p
licat
io
n
o
f
f
r
ac
tal
in
te
r
p
o
latio
n
h
a
s
also
b
ee
n
wid
ely
ca
r
r
ied
o
u
t
in
v
ar
i
o
u
s
f
ield
s
.
An
aly
s
is
o
f
co
r
o
n
av
ir
u
s
d
is
ea
s
e
2
0
1
9
(
C
OVI
D
-
19
)
s
p
r
ea
d
u
s
in
g
f
r
ac
tal
in
ter
p
o
latio
n
[
1
1
]
.
An
al
y
s
is
r
an
d
o
m
d
ata
s
et
u
s
in
g
f
r
ac
tal
in
ter
p
o
latio
n
f
u
n
ctio
n
(
FIF)
[
1
2
]
–
[
1
4
]
.
Seis
m
ic
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
6
,
No
.
3
,
Dec
em
b
er
20
24
:
1
4
8
5
-
1
4
92
1486
tr
ac
es
u
s
in
g
f
r
ac
ta
l
in
ter
p
o
lati
o
n
with
v
er
tical
s
ca
le
f
ac
to
r
an
d
r
esid
u
al
b
e
h
av
io
r
[
1
5
]
.
I
n
th
is
s
tu
d
y
,
f
r
ac
tal
in
ter
p
o
latio
n
was
ap
p
lied
to
d
eter
m
in
e
th
e
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al
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o
f
t
h
e
d
em
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d
p
ar
a
m
eter
ap
p
r
o
ac
h
in
th
e
in
v
en
to
r
y
m
o
d
el.
T
h
e
f
r
ac
tal
in
ter
p
o
latio
n
v
alu
e
is
in
f
lu
en
ce
d
b
y
th
e
v
er
tical
s
ca
le
f
ac
to
r
an
d
FIF.
Ma
n
y
s
tu
d
ies
o
n
f
r
ac
tal
in
ter
p
o
latio
n
h
a
v
e
b
ee
n
ca
r
r
ied
o
u
t.
Ve
r
tical
s
ca
lin
g
f
ac
to
r
im
p
r
o
v
em
en
t
i
n
f
r
ac
tal
in
ter
p
o
latio
n
t
o
p
r
ed
ict
in
n
a
v
ig
atio
n
s
y
s
tem
[
1
6
]
.
I
m
p
r
o
v
e
FIF
u
s
in
g
box
-
co
u
n
tin
g
d
im
en
s
io
n
with
f
u
n
ctio
n
c
o
n
tr
ac
tiv
ity
f
ac
to
r
s
[
1
7
]
,
[
1
8
]
.
C
o
n
s
tr
u
ct
FIF
with
iter
ated
f
u
n
ctio
n
s
y
s
tem
(
I
FS
)
[
1
9
]
.
R
atio
n
al
c
u
b
i
c
tr
ig
o
n
o
m
et
r
ic
FIF
th
at
ar
e
th
e
g
en
er
alize
d
f
r
ac
tal
v
er
s
io
n
o
f
th
e
class
ical
r
atio
n
al
cu
b
ic
tr
ig
o
n
o
m
et
r
ic
p
o
ly
n
o
m
ial
s
p
lin
e
[
2
0
]
.
Gen
er
alize
d
tr
ig
o
n
o
m
etr
ic
f
u
n
ctio
n
as
FIF
[
2
1
]
.
Ri
[
2
2
]
,
[
2
3
]
in
tr
o
d
u
ce
a
n
ew
id
ea
to
co
n
s
tr
u
ct
th
e
n
o
n
lin
ea
r
FIF.
C
o
n
s
tr
u
ct
FIF
with
m
u
lti
v
ar
iate
af
f
in
e
f
u
n
ctio
n
[
2
4
]
.
FIF
with
n
o
n
-
af
f
in
e
f
u
n
ctio
n
[
2
5
]
.
C
o
n
s
tr
u
ct
FIF
with
g
ask
et
Sier
s
p
in
s
k
i
[
2
6
]
,
[
2
7
]
in
tr
o
d
u
ce
n
ew
s
u
r
f
ac
e
FIF.
FIF
co
n
s
tr
u
ctio
n
is
a
v
er
y
im
p
o
r
tan
t
p
ar
t
in
f
r
ac
tal
in
ter
p
o
lat
io
n
.
Pre
v
io
u
s
s
tu
d
ies
h
av
e
s
h
o
wn
th
at
s
ev
er
al
f
u
n
ctio
n
s
ca
n
b
e
u
s
ed
as
FIF,
in
clu
d
in
g
n
o
n
lin
ea
r
an
d
tr
ig
o
n
o
m
etr
ic
f
u
n
ctio
n
s
.
T
h
is
r
esear
ch
in
tr
o
d
u
ce
s
f
r
ac
tal
in
ter
p
o
latio
n
t
ec
h
n
iq
u
es
with
t
h
e
d
ev
elo
p
m
e
n
t
o
f
FIF
co
n
s
tr
u
c
ted
f
r
o
m
th
e
Sier
p
in
s
k
i
tr
ian
g
le.
T
h
e
Sier
p
in
s
k
i
tr
ian
g
le
is
a
f
r
ac
tal
s
h
ap
e
co
n
s
tr
u
cted
f
r
o
m
af
f
in
e
f
u
n
ct
io
n
s
.
T
h
e
FIF
o
f
t
h
e
Sier
p
in
s
k
i
tr
ian
g
le
co
n
s
is
ts
o
f
th
r
ee
a
f
f
in
e
f
u
n
ctio
n
s
th
at
m
ap
th
e
in
itial tr
ian
g
le
in
to
a
n
ew
tr
ian
g
le
with
h
alf
th
e
s
ize
o
f
th
e
p
r
e
v
io
u
s
tr
ian
g
le.
I
n
f
r
a
ctal
in
ter
p
o
latio
n
,
a
g
u
ar
an
tee
o
f
t
h
e
ex
is
ten
ce
o
f
th
e
attr
ac
to
r
is
r
eq
u
ir
ed
.
Ri
[
2
6
]
,
[
2
7
]
h
as
g
u
a
r
an
teed
t
h
e
ex
is
ten
ce
o
f
an
attr
ac
to
r
f
r
o
m
g
ask
et
Sier
p
i
n
s
k
i.
T
h
e
Sier
p
i
n
s
k
i
t
r
ian
g
le
is
p
ar
t
o
f
th
e
Sier
p
in
s
k
i
g
ask
et,
t
h
u
s
en
s
u
r
in
g
t
h
at
th
e
FIF
b
u
ilt
f
r
o
m
th
e
Sier
p
in
s
k
i
tr
ian
g
le
ca
n
in
ter
p
o
late
th
e
d
ata.
I
n
ter
p
o
latio
n
tech
n
i
q
u
es
ca
n
b
e
u
s
ed
to
d
eter
m
in
e
th
e
ap
p
r
o
x
im
at
e
v
alu
e
o
f
p
ar
am
eter
s
th
at
ar
e
n
o
t
k
n
o
w
n
with
ce
r
tain
ty
,
s
u
ch
as
th
e
d
em
an
d
p
ar
am
eter
in
th
e
in
v
en
to
r
y
m
o
d
el.
Gen
er
ally
,
th
e
v
alu
e
o
f
th
e
d
em
an
d
p
ar
am
eter
in
t
h
e
in
v
en
to
r
y
m
o
d
el
is
d
eter
m
in
ed
b
y
f
o
r
ec
asti
n
g
te
ch
n
iq
u
es.
I
n
th
is
s
tu
d
y
,
th
e
u
n
ce
r
tain
ty
ap
p
r
o
a
ch
to
th
e
d
e
m
an
d
p
ar
am
eter
is
d
eter
m
in
ed
u
s
in
g
f
r
ac
tal
in
ter
p
o
latio
n
.
Fo
r
f
u
r
t
h
er
i
n
f
o
r
m
atio
n
,
a
n
i
n
ter
p
o
latio
n
ca
lcu
latio
n
u
s
in
g
r
ice
s
u
p
p
ly
d
ata
is
p
r
o
v
id
e
d
.
2.
M
E
T
H
O
D
I
n
th
is
r
esear
ch
,
f
r
ac
tal
i
n
ter
p
o
latio
n
m
eth
o
d
is
in
tr
o
d
u
ce
d
with
FIF
wh
ich
is
co
n
s
tr
u
c
ted
f
r
o
m
Sier
s
p
in
s
k
i
t
r
ian
g
le.
T
h
e
f
o
llo
win
g
is
th
e
FIF
f
o
r
m
u
latio
n
o
f
th
e
Sier
s
p
in
s
k
i
t
r
ian
g
le
:
:
ℝ
2
→
ℝ
2
,
=
{
1
,
2
,
3
}
1
(
[
]
)
=
[
0
.
5
0
0
0
.
5
]
[
]
(
1
)
2
(
[
]
)
=
[
0
.
5
0
0
0
.
5
]
[
]
+
[
0
0
.
5
]
(
2
)
3
(
[
]
)
=
[
0
.
5
0
0
0
.
5
]
[
]
+
[
0
.
5
0
]
(
3
)
1
m
ap
s
th
e
in
itial
S
ier
s
p
in
s
k
i
tr
i
an
g
le
in
to
co
n
g
r
u
en
t
tr
ian
g
les
with
a
s
ize
0
.
5
s
m
aller
th
an
t
h
e
in
itial
s
h
ap
e.
T
h
e
2
f
u
n
ctio
n
m
ap
s
th
e
in
itial
s
h
ap
e
with
a
s
ize
0
.
5
s
m
all
er
th
an
th
e
in
itial
s
h
ap
e
an
d
th
en
s
h
if
ts
it
u
p
p
ar
allel
to
t
h
e
v
e
r
tical
ax
is
b
y
0
.
5
u
n
its
.
T
h
e
3
f
u
n
ctio
n
m
ap
s
t
h
e
in
itial
s
h
ap
e
in
to
a
n
ew
tr
ia
n
g
le
with
a
s
ize
0
.
5
s
m
aller
th
an
th
e
in
itial tr
ia
n
g
le
an
d
s
h
if
ted
to
th
e
r
ig
h
t
p
a
r
allel
to
th
e
h
o
r
izo
n
tal
ax
is
b
y
0
.
5
u
n
its
.
T
h
e
f
o
llo
win
g
is
a
f
r
ac
tal
in
ter
p
o
latio
n
alg
o
r
ith
m
with
FIF
c
o
n
s
tr
u
cted
f
r
o
m
Sier
s
p
in
s
k
i tr
i
an
g
les.
a)
Giv
en
th
e
in
itial
d
ata
{
(
,
)
∈
ℝ
2
:
=
1
,
2
,
3
}
,
1
<
2
<
3
an
d
th
e
n
u
m
b
er
o
f
iter
atio
n
s
d
esire
d
.
T
h
e
in
itial
co
n
d
itio
n
s
(
,
)
ar
e
tak
en
b
ased
o
n
th
e
d
ata.
T
h
e
s
elec
tio
n
o
f
in
itial
co
n
d
itio
n
s
is
b
ased
o
n
th
e
co
n
s
id
er
at
io
n
th
at
th
e
tr
ian
g
u
l
ar
r
eg
io
n
d
escr
ib
ed
f
r
o
m
th
e
th
r
ee
in
itial
co
n
d
itio
n
s
will
in
c
lu
d
e
all
v
alu
es
in
th
e
d
ata.
T
h
is
is
r
elate
d
to
th
e
ca
lcu
latio
n
o
f
th
e
er
r
o
r
v
al
u
e.
b)
Dete
r
m
in
e
d
is
tan
ce
1
,
2
,
3
an
d
d
is
tan
ce
1
,
2
,
3
:
1
=
|
1
−
2
|
,
2
=
|
1
−
3
|
,
3
=
|
2
−
3
|
4
=
|
1
−
2
|
,
5
=
|
1
−
3
|
,
6
=
|
2
−
3
|
Dis
tan
ce
ca
lcu
latio
n
s
ar
e
n
ee
d
ed
to
d
eter
m
i
n
e
th
e
v
alu
es
[
∗
∗
]
.
c)
Dete
r
m
in
e
1
(
[
∗
∗
]
)
b
ased
o
n
(
1
)
,
2
(
[
∗
∗
]
)
b
ased
o
n
(
2
)
,
a
n
d
3
(
[
∗
∗
]
)
b
ased
o
n
(
3
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
I
mp
r
o
ve
fr
a
cta
l in
terp
o
la
tio
n
fu
n
ctio
n
w
ith
S
iers
p
in
s
ki
tr
ia
n
g
le
(
E
ka
S
u
s
a
n
ti
)
1487
d)
W
e
g
et
a
n
ew
tr
ian
g
le
∗
=
⋃
(
∗
)
=
1
(
∗
)
3
=
1
∪
2
(
∗
)
∪
3
(
∗
)
e)
T
h
e
iter
atio
n
is
co
n
tin
u
ed
a
n
d
r
etu
r
n
s
to
Step
2
.
f)
∗
is
a
n
ew
tr
ian
g
le
with
th
e
in
ter
p
o
lated
p
o
in
ts
.
A
n
ew
tr
ian
g
le
is
o
b
tain
ed
th
r
ee
tr
ian
g
le
t
h
at
is
h
alf
th
e
s
ize
o
f
th
e
p
r
e
v
io
u
s
tr
ian
g
le.
I
t
er
atio
n
s
ca
n
b
e
c
o
n
tin
u
e
d
u
n
til th
e
ex
p
ec
ted
er
r
o
r
v
alu
e
is
o
b
tain
ed
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
ap
p
licatio
n
o
f
f
r
ac
tal
in
ter
p
o
latio
n
tech
n
iq
u
e
aim
s
to
d
eter
m
in
e
th
e
ap
p
r
o
x
im
ate
v
alu
e
o
f
th
e
d
em
an
d
p
a
r
am
eter
in
th
e
in
v
en
to
r
y
m
o
d
el.
I
n
th
is
s
tu
d
y
,
f
r
ac
tal
in
ter
p
o
latio
n
tech
n
iq
u
es
wer
e
ap
p
lied
to
d
eter
m
in
e
th
e
v
alu
e
o
f
r
ice
d
e
m
an
d
p
a
r
am
eter
s
in
a
co
m
p
an
y
.
B
ased
o
n
th
e
d
ata
i
n
T
a
b
le
1
tak
en
(
1
0
0
0
0
,
3
1
3
8
6
7
9
)
,
(
1
0
8
0
0
,
1
1
7
7
7
3
3
)
,
(
1
2
0
0
0
,
3
6
2
4
0
0
)
as
th
e
in
itial
co
n
d
itio
n
t
o
p
e
r
f
o
r
m
f
r
ac
tal
in
ter
p
o
latio
n
with
FIF
b
u
ilt
f
r
o
m
Sier
s
p
in
s
k
i
tr
ian
g
les.
T
h
is
v
alu
e
is
tak
e
n
f
r
o
m
t
h
e
lo
west
an
d
h
ig
h
est
p
r
ices
an
d
o
n
e
m
o
r
e
p
o
in
t
is
tak
en
b
y
c
o
n
s
id
er
in
g
th
e
i
n
itial
tr
ian
g
le
f
o
r
m
e
d
wh
ich
ca
n
co
v
er
th
e
d
ata
ar
ea
.
T
h
e
in
itial
co
n
d
i
tio
n
s
elec
tio
n
is
n
o
t
s
in
g
le,
th
r
ee
o
t
h
er
p
ai
r
s
o
f
p
o
i
n
ts
in
t
h
e
d
ata
ca
n
also
b
e
s
elec
ted
,
s
u
ch
as
(
1
0
0
0
0
,
3
1
3
8
6
7
9
)
,
(
1
0
1
5
0
,
1
5
1
2
2
9
9
)
,
(
1
2
0
0
0
,
3
6
2
4
0
0
)
as
th
e
in
itial
co
n
d
itio
n
.
Ho
wev
e
r
,
af
ter
ca
r
r
y
in
g
o
u
t
th
e
ca
lcu
latio
n
s
,
it
ca
n
b
e
s
ee
n
f
r
o
m
th
e
n
u
m
b
e
r
o
f
iter
atio
n
s
th
at
s
elec
tio
n
(
1
0
0
0
0
,
3
1
3
8
6
7
9
)
,
(
1
0
8
0
0
,
1
1
7
7
7
3
3
)
,
(
1
2
0
0
0
,
3
6
2
4
0
0
)
as
th
e
s
tar
tin
g
p
o
in
t
is
m
o
r
e
o
p
tim
al.
T
h
e
f
o
llo
win
g
is
th
e
ca
lcu
latio
n
s
tag
e
f
o
r
iter
atio
n
1
.
a)
L
et
1
=
10000
;
1
=
3138679
;
2
=
10800
;
2
=
1177733
;
3
=
12000
;
3
=
362
400
.
A
s
k
etch
o
f
th
e
Sier
p
in
s
k
i
t
r
ia
n
g
le
im
ag
e
b
ased
o
n
t
h
e
in
itial c
o
n
d
itio
n
s
g
iv
en
in
Fig
u
r
e
1
.
T
ab
le
1
.
Data
o
n
p
r
ices a
n
d
d
e
m
an
d
P
e
r
i
o
d
(
m
o
n
t
h
)
P
r
i
c
e
(
I
D
R
)
D
e
man
d
(
k
i
l
o
g
r
a
m)
1
1
0
5
0
0
1
8
7
7
8
1
9
2
1
0
1
5
0
1
5
1
2
2
9
9
3
1
0
8
0
0
1
1
7
7
7
3
3
4
1
1
5
5
0
1
4
0
5
4
3
5
5
1
1
4
0
0
2
4
1
9
0
6
9
6
1
2
0
0
0
3
6
2
4
0
0
7
1
0
2
5
0
1
9
6
6
1
6
9
8
1
0
5
0
0
1
8
4
8
0
8
4
9
1
0
4
0
0
1
4
4
9
5
7
0
10
1
1
8
0
0
9
2
3
0
4
9
11
1
0
3
5
0
2
1
1
9
5
9
8
12
1
0
0
0
0
3
1
3
8
6
7
9
Fig
u
r
e
1
.
Sier
p
in
s
k
i
tr
ia
n
g
le
it
er
atio
n
0
F
i
g
u
r
e
1
i
s
a
n
i
n
i
t
i
a
l
t
r
i
a
n
g
l
e
f
o
r
m
e
d
b
a
s
e
d
o
n
p
a
i
r
s
o
f
p
o
i
n
t
s
a
s
i
n
i
t
i
a
l
c
o
n
d
i
t
i
o
n
s
.
N
e
x
t
,
u
s
i
n
g
(
1
)
-
(
3
)
th
e
Sier
s
p
in
s
k
i tr
ian
g
le
will b
e
f
o
r
m
e
d
.
b)
Dete
r
m
in
e
th
e
d
is
tan
ce
to
th
e
an
d
ax
es
1
=
|
1
−
2
|
=
|
10000
−
10800
|
=
800
2
=
|
1
−
3
|
=
|
10000
−
12000
|
=
2000
3
=
|
2
−
3
|
=
|
10800
−
12000
|
=
1200
4
=
|
1
−
2
|
=
|
3138679
−
1177733
|
=
1960946
5
=
|
1
−
3
|
=
|
3138679
−
362400
|
=
2776279
6
=
|
2
−
3
|
=
|
1177733
−
362400
|
=
815333
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
6
,
No
.
3
,
Dec
em
b
er
20
24
:
1
4
8
5
-
1
4
92
1488
T
h
e
d
is
tan
ce
s
1
,
2
an
d
3
ar
e
u
s
ed
to
d
eter
m
in
e
t
h
e
tr
an
s
lati
o
n
ab
o
u
t
th
e
h
o
r
izo
n
tal
a
x
is
.
W
h
ile
th
e
d
is
tan
ce
s
4
,
5
,
an
d
6
ar
e
u
s
ed
to
d
eter
m
in
e
th
e
tr
a
n
s
latio
n
ab
o
u
t
th
e
v
er
tical
ax
is
.
Usi
n
g
FI
F
(
1
)
-
(
3
)
w
e
will g
et
[
∗
∗
]
as th
e
n
ew
in
itial c
o
n
d
itio
n
.
c)
Dete
r
m
in
e
in
ter
p
o
latio
n
v
alu
e
b
ased
o
n
FIF
(
1
)
,
(
2
)
,
a
n
d
(
3
)
.
I
n
ter
p
o
latio
n
is
p
er
f
o
r
m
ed
o
n
(
1
0
0
0
0
,
3
1
3
8
6
7
9
)
,
(
1
0
8
0
0
,
1
1
7
7
7
3
3
)
,
(
1
2
0
0
0
,
3
6
2
4
0
0
)
u
s
e
th
e
1
f
u
n
ctio
n
.
1
(
1
∗
,
1
∗
)
=
(
1
+
1
2
|
2
−
1
|
,
1
−
1
2
|
2
−
1
|
)
=
(
10000
+
0
,
5
(
400
)
,
3138679
−
0
,
5
(
19609
46
)
)
=
(
10400
,
2158206
)
O
b
tain
ed
1
(
1
∗
,
1
∗
)
=
(
10400
,
2158206
)
1
(
2
∗
,
2
∗
)
=
(
2
,
2
)
=
(
10800
,
1177733
)
1
(
3
∗
,
3
∗
)
=
(
3
−
1
2
|
3
−
2
|
,
3
+
1
2
|
3
−
2
|
)
=
(
12000
−
0
,
5
(
1200
)
,
362400
+
0
,
5
(
815333
)
)
=
(
11400
,
770067
)
O
b
tain
ed
1
(
3
∗
,
3
∗
)
=
(
1140
0
,
770067
)
I
n
ter
p
o
latio
n
is
p
er
f
o
r
m
ed
o
n
(
10000
,
3138679
)
,
(
10800
,
1177733
)
,
(
1200
0
,
362400
)
u
s
e
th
e
2
.
2
(
1
∗
,
1
∗
)
=
(
1
,
1
)
=
(
1000
0
,
3138679
)
2
(
2
∗
,
2
∗
)
=
1
(
1
∗
,
1
∗
)
=
(
10400
,
2158206
)
2
(
3
∗
,
3
∗
)
=
(
3
−
1
2
|
1
−
3
|
,
3
+
1
2
|
1
−
3
|
)
=
(
12000
−
0
,
5
(
2000
)
,
362400
+
0
,
5
(
2776279
)
)
=
(
11000
,
1750539
)
I
n
ter
p
o
latio
n
r
esu
lts
ar
e
o
b
tain
ed
2
(
3
∗
,
3
∗
)
=
(
11000
,
1750539
)
.
I
n
ter
p
o
latio
n
is
p
er
f
o
r
m
ed
o
n
(
10000
,
3138679
)
,
(
10800
,
1177733
)
,
(
12000
,
362400
)
u
s
e
th
e
3
.
3
(
1
∗
,
1
∗
)
=
2
(
2
∗
,
2
∗
)
=
(
1040
0
,
2158206
)
3
(
2
∗
,
2
∗
)
=
1
(
3
∗
,
3
∗
)
=
(
11400
,
770067
)
3
(
3
∗
,
3
∗
)
=
(
3
,
3
)
=
(
12000
,
362400
)
Usi
n
g
1
an
d
th
e
in
itial
co
n
d
iti
o
n
s
g
iv
en
,
th
e
in
ter
p
o
lated
v
alu
es
ar
e
o
b
tain
ed
(
1
0
4
0
0
,
2
1
5
8
2
0
6
)
,
(
1
0
8
0
0
,
1
1
7
7
7
3
3
)
,
(
1
1
4
0
0
,
7
7
0
0
6
7
)
.
Usi
n
g
2
we
g
et
(
1
0
0
0
0
,
3
1
3
8
6
7
9
)
,
(
1
0
4
0
0
,
2
1
5
8
2
0
6
)
,
(
1
1
0
0
0
,
1
7
5
0
5
3
9
)
an
d
with
3
we
g
et
(
1
0
4
0
0
,
2
1
5
8
2
0
6
)
,
(
1
1
4
0
0
,
7
7
0
0
6
7
)
,
(
1
2
0
0
0
,
3
6
2
4
0
0
)
.
T
h
e
Sier
s
p
in
s
k
i
tr
ian
g
le
im
ag
e
r
esu
ltin
g
f
r
o
m
i
ter
atio
n
1
is
g
iv
en
in
Fig
u
r
e
2
.
Fig
u
r
e
1
is
a
n
ew
tr
ian
g
le
with
h
alf
th
e
s
ize
o
f
th
e
p
r
ev
i
o
u
s
tr
ian
g
le
an
d
ig
n
o
r
in
g
th
e
m
id
d
le
p
ar
t.
I
n
i
ter
atio
n
1
,
ea
ch
i
n
itial
co
n
d
it
io
n
will
b
e
m
ap
p
e
d
b
y
th
e
f
u
n
ctio
n
s
1
,
2
an
d
3
s
o
th
at
th
r
ee
n
ew
co
n
g
r
u
en
t
tr
ian
g
les
ar
e
o
b
tain
ed
.
Usi
n
g
t
h
e
s
am
e
s
tep
s
in
iter
atio
n
1
,
t
h
e
ca
lcu
latio
n
is
co
n
tin
u
ed
f
o
r
iter
atio
n
2
a
n
d
s
o
o
n
.
As a
v
is
u
aliza
tio
n
f
o
r
th
e
i
n
ter
p
o
latio
n
s
tag
es,
th
e
Sier
s
p
i
n
s
k
i tr
ian
g
le
iter
atio
n
2
is
g
iv
e
n
.
Fig
u
r
e
3
is
th
e
Sier
s
p
in
s
k
i
tr
ian
g
le
r
esu
ltin
g
f
r
o
m
th
e
in
te
r
p
o
latio
n
o
f
i
ter
atio
n
2
.
T
h
e
r
e
ar
e
n
in
e
n
ew
tr
ian
g
les
an
d
twen
ty
-
s
ev
en
p
a
ir
s
o
f
p
o
in
ts
wh
ich
ar
e
th
e
in
itial
co
n
d
itio
n
s
f
o
r
th
e
iter
atio
n
2
.
T
h
e
co
m
p
lete
in
ter
p
o
latio
n
r
esu
lts
o
f
iter
atio
n
1
an
d
iter
atio
n
2
ar
e
g
iv
en
in
T
ab
le
2
.
Fig
u
r
e
2
.
Sier
p
in
s
k
i
tr
ia
n
g
le
it
er
atio
n
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
I
mp
r
o
ve
fr
a
cta
l in
terp
o
la
tio
n
fu
n
ctio
n
w
ith
S
iers
p
in
s
ki
tr
ia
n
g
le
(
E
ka
S
u
s
a
n
ti
)
1489
Fig
u
r
e
3
.
Sier
p
in
s
k
i
tr
ia
n
g
le
it
er
atio
n
2
T
ab
le
2
.
I
n
ter
p
o
latio
n
r
esu
lts
o
f
iter
atio
n
1
an
d
iter
atio
n
2
P
r
i
c
e
(
I
D
R
)
D
e
man
d
(
k
i
l
o
g
r
a
m)
D
e
man
d
i
n
t
e
r
p
o
l
a
t
i
o
n
o
f
i
t
e
r
a
t
i
o
n
1
D
e
man
d
i
n
t
e
r
p
o
l
a
t
i
o
n
o
f
i
t
e
r
a
t
i
o
n
1
1
0
5
0
0
1
8
7
7
8
1
9
1
0
1
5
0
1
5
1
2
2
9
9
1
0
8
0
0
1
1
7
7
7
3
3
1
1
7
7
7
3
3
1
1
7
7
7
3
3
1
1
5
5
0
1
4
0
5
4
3
5
1
1
4
0
0
2
4
1
9
0
6
9
1
2
0
0
0
3
6
2
4
0
0
3
6
2
4
0
0
3
6
2
4
0
0
1
0
2
5
0
1
9
6
6
1
6
9
1
0
5
0
0
1
8
4
8
0
8
4
2
4
4
4
6
0
9
1
0
4
0
0
1
4
4
9
5
7
0
2
1
5
8
2
0
6
2
1
5
8
2
0
6
2
1
5
8
2
0
6
2
1
5
8
2
0
6
2
1
5
8
2
0
6
2
1
5
8
2
0
6
1
1
8
0
0
9
2
3
0
4
9
1
0
3
5
0
2
1
1
9
5
9
8
1
0
0
0
0
3
1
3
8
6
7
9
3
1
3
8
6
7
9
3
1
3
8
6
7
9
1
0
.
2
0
0
2
6
2
8
4
4
3
2
6
2
8
4
4
3
2
6
2
8
4
4
3
1
0
.
6
0
0
1
6
6
7
9
7
0
1
6
6
7
9
7
0
1
6
6
7
9
7
0
1
0
.
7
0
0
1
9
5
4
3
7
3
1
9
5
4
3
7
3
1
0
.
8
0
0
1
1
7
7
7
3
3
1
0
.
9
0
0
1
4
6
4
1
3
7
1
4
6
4
1
3
7
1
4
6
4
1
3
7
1
4
6
4
1
3
7
1
1
.
0
0
0
1
7
5
0
5
3
9
1
7
5
0
5
3
9
1
1
.
1
0
0
9
7
3
9
0
0
9
7
3
9
0
0
1
1
.
2
0
0
1
2
6
0
3
0
3
1
1
.
4
0
0
7
7
0
0
6
7
7
7
0
0
6
7
7
7
0
0
6
7
1
1
.
7
0
0
5
6
6
2
3
4
5
6
6
2
3
4
I
n
T
ab
le
2
,
th
e
in
ter
p
o
latio
n
r
esu
lts
ar
e
p
r
esen
ted
in
th
e
f
o
r
m
o
f
a
r
ice
d
em
an
d
v
alu
e
a
p
p
r
o
ac
h
.
I
n
iter
atio
n
1
,
t
h
e
d
em
a
n
d
a
p
p
r
o
ac
h
v
alu
es
ar
e
o
b
tain
e
d
f
o
r
p
r
ices
o
f
1
0
8
0
0
,
1
2
0
0
0
,
1
0
4
0
0
,
1
0
0
0
0
,
1
1
0
0
,
a
n
d
1
1
4
0
0
.
I
n
iter
atio
n
2
,
ap
p
r
o
x
i
m
ate
v
alu
es
f
o
r
th
e
r
ice
p
r
ic
es
wer
e
o
b
tain
ed
:
1
0
5
0
0
,
1
0
8
0
0
,
1
1
4
0
0
,
1
0
4
0
0
,
1
0
0
0
0
,
1
1
0
0
0
,
1
1
2
0
0
,
1
1
7
0
0
,
1
0
2
0
0
,
1
0
6
0
0
,
1
0
7
0
0
,
an
d
1
0
9
0
0
.
Up
to
iter
atio
n
2
,
MA
PE
ca
n
n
o
t
b
e
ca
lcu
lated
b
ec
au
s
e
th
e
ap
p
r
o
ac
h
f
o
r
s
ev
e
r
al
p
r
ices
in
T
ab
le
1
is
n
o
t
y
et
av
ailab
le.
T
h
e
r
ef
o
r
e,
t
h
e
iter
atio
n
co
n
tin
u
es
u
n
til
th
e
MA
PE
ca
lcu
latio
n
ca
n
b
e
ca
r
r
ied
o
u
t
an
d
th
e
e
x
p
ec
ted
le
v
el
o
f
ac
cu
r
ac
y
is
ac
h
iev
e
d
.
B
ased
o
n
th
e
d
ata,
a
b
etter
le
v
el
o
f
ac
cu
r
ac
y
was
ac
h
iev
ed
in
i
ter
atio
n
9
c
o
m
p
ar
e
d
to
i
te
r
atio
n
s
6
,
7
,
a
n
d
8
.
Fig
u
r
e
4
,
v
is
u
alizin
g
i
ter
atio
n
9
.
Fig
u
r
e
2
d
ep
icts
th
e
r
esu
lt o
f
t
h
e
1
st
iter
atio
n
o
f
in
ter
p
o
latio
n
,
wh
er
e
3
s
im
ilar
tr
ian
g
les an
d
9
p
air
s
o
f
p
o
in
ts
ar
e
o
b
tain
e
d
.
Fig
u
r
e
3
d
is
p
lay
s
th
e
Sier
p
in
s
k
i
tr
ian
g
l
e
ac
q
u
ir
e
d
f
r
o
m
th
e
2
nd
iter
ati
o
n
o
f
i
n
ter
p
o
latio
n
,
y
ield
in
g
9
n
ew
tr
ian
g
les
with
2
7
p
ai
r
s
o
f
p
o
in
ts
.
I
n
th
e
th
ir
d
iter
atio
n
,
2
7
n
ew
tr
ian
g
les
an
d
8
1
p
o
in
t
p
air
s
will
b
e
o
b
tain
ed
,
an
d
s
o
o
n
.
Fo
r
th
e
n
-
th
iter
atio
n
,
it
ca
n
b
e
e
x
p
r
ess
ed
as
3
tr
ian
g
les,
wh
er
e
n
r
ep
r
esen
ts
th
e
n
u
m
b
er
o
f
iter
atio
n
s
.
T
h
e
n
u
m
b
er
o
f
p
air
s
o
f
in
te
r
p
o
latio
n
p
o
in
ts
g
e
n
er
at
ed
is
3
+
1
.
T
h
e
le
v
el
o
f
ac
cu
r
ac
y
is
d
eter
m
in
ed
u
s
in
g
MA
PE,
an
d
th
e
ca
lcu
latio
n
o
f
f
r
ac
tal
in
ter
p
o
latio
n
an
d
v
is
u
aliza
tio
n
is
co
n
d
u
cte
d
u
s
in
g
Py
th
o
n
p
r
o
g
r
am
m
i
n
g
.
T
h
e
f
o
llo
win
g
ar
e
th
e
v
alu
es
o
f
th
e
d
em
an
d
p
ar
am
ete
r
ap
p
r
o
ac
h
b
ased
o
n
f
r
ac
tal
in
ter
p
o
latio
n
f
o
r
iter
atio
n
s
6
,
7
,
8
,
an
d
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
6
,
No
.
3
,
Dec
em
b
er
20
24
:
1
4
8
5
-
1
4
92
1490
Fig
u
r
e
4
.
Sier
p
in
s
k
i
tr
ia
n
g
le
it
er
atio
n
9
I
n
T
ab
le
3
,
th
e
in
ter
p
o
latio
n
r
esu
lts
ar
e
p
r
o
v
id
ed
f
o
r
th
e
r
ic
e
p
r
ices
lis
ted
in
T
ab
le
1
.
B
as
ed
o
n
th
e
d
ata
in
T
ab
le
1
,
MA
PE
v
al
u
es
ca
n
b
e
ca
lcu
lated
s
tar
tin
g
f
r
o
m
iter
atio
n
6
.
I
n
th
is
s
tu
d
y
,
in
ter
p
o
latio
n
ca
lcu
latio
n
s
wer
e
ca
r
r
ied
o
u
t
u
p
to
iter
atio
n
9
.
T
h
e
MA
PE
v
alu
es
o
b
tain
e
d
f
o
r
iter
atio
n
s
6
to
9
ar
e
2
4
.
6
0
3
%,
2
4
.
6
0
3
%,
2
3
.
8
5
8
%,
an
d
2
3
.
7
7
2
%,
r
esp
ec
tiv
ely
.
Usi
n
g
th
e
FIF
co
n
s
tr
u
cted
f
r
o
m
th
e
Sier
p
in
s
k
i
tr
ian
g
le,
th
e
MA
PE
v
alu
es
m
ee
t
th
e
s
u
f
f
icien
t
cr
iter
ia.
T
h
er
e
is
a
d
ec
r
ea
s
e
in
th
e
MA
PE
v
alu
e,
in
d
icatin
g
an
in
cr
ea
s
e
in
th
e
ac
cu
r
ac
y
v
al
u
e
f
o
r
t
h
e
in
t
er
p
o
latio
n
s
tag
es
with
h
ig
h
er
iter
atio
n
s
.
Ho
wev
er
,
th
e
d
ec
r
ea
s
e
in
th
e
MA
PE
v
alu
e
f
r
o
m
iter
atio
n
6
to
iter
at
io
n
9
is
n
o
t sig
n
i
f
ican
t a
n
d
r
e
m
ain
s
with
in
th
e
s
u
f
f
icien
t c
r
it
er
ia.
T
h
is
p
ap
er
in
tr
o
d
u
ce
s
an
in
ter
p
o
l
atio
n
tech
n
iq
u
e
with
th
e
d
ev
elo
p
m
en
t
o
f
FIF
u
s
in
g
af
f
in
e
m
ap
p
in
g
to
co
n
s
tr
u
ct
Sier
p
in
s
k
i
tr
ian
g
les.
I
n
s
h
o
r
t,
f
r
ac
tal
in
ter
p
o
lati
o
n
with
FIF,
b
u
ilt
f
r
o
m
th
e
af
f
in
e
m
ap
p
in
g
s
1
,
2
an
d
3
,
f
o
r
m
s
a
n
ew
tr
ian
g
le
h
a
lf
th
e
s
ize
o
f
th
e
p
r
e
v
io
u
s
o
n
e,
ig
n
o
r
in
g
th
e
m
id
d
le
p
a
r
t.
T
h
e
p
air
o
f
p
o
in
ts
f
o
r
m
in
g
th
e
tr
ian
g
le
r
esu
lts
f
r
o
m
in
ter
p
o
latio
n
.
C
alcu
lativ
ely
,
th
is
in
ter
p
o
latio
n
tech
n
iq
u
e
is
r
elativ
ely
ea
s
y
to
ap
p
ly
,
y
et
th
e
lev
el
o
f
ac
cu
r
ac
y
o
b
tain
ed
s
till
m
ee
ts
th
e
s
u
f
f
icien
t
cr
iter
ia.
T
h
e
d
ev
el
o
p
ed
in
ter
p
o
latio
n
tech
n
iq
u
e
is
ap
p
lied
to
d
eter
m
in
e
th
e
a
p
p
r
o
x
im
ate
v
alu
e
o
f
t
h
e
d
em
a
n
d
d
ata,
wh
ic
h
ca
n
b
e
u
s
ed
to
ascer
tain
th
e
u
n
ce
r
tain
ty
o
f
d
em
an
d
p
ar
am
eter
v
alu
es in
th
e
i
n
v
en
to
r
y
m
o
d
el.
T
ab
le
3
.
Dem
an
d
f
r
ac
tal
i
n
ter
p
o
latio
n
r
esu
lts
D
e
man
d
(
k
i
l
o
g
r
a
m)
D
e
man
d
i
n
t
e
r
p
o
l
a
t
i
o
n
o
f
i
t
e
r
a
t
i
o
n
s
6
a
n
d
7
(
k
i
l
o
g
r
a
m)
D
e
man
d
i
n
t
e
r
p
o
l
a
t
i
o
n
o
f
i
t
e
r
a
t
i
o
n
s
8
(
k
i
l
o
g
r
a
m)
D
e
man
d
i
n
t
e
r
p
o
l
a
t
i
o
n
o
f
i
t
e
r
a
t
i
o
n
s
9
(
k
i
l
o
g
r
a
m)
1
8
7
7
8
1
9
1
9
1
3
0
8
7
.
6
1
9
1
3
0
8
7
.
6
1
9
1
3
0
8
7
.
6
1
5
1
2
2
9
9
2
7
7
1
0
0
1
.
2
2
7
7
1
0
0
1
.
2
2
7
7
1
0
0
1
.
2
1
1
7
7
7
3
3
1
1
7
7
7
3
3
.
0
1
1
7
7
7
3
3
1
1
7
7
7
3
3
1
4
0
5
4
3
5
9
3
3
9
1
0
.
5
9
8
3
7
4
0
.
7
9
8
3
7
4
0
.
7
2
4
1
9
0
6
9
1
1
6
8
7
0
7
.
5
1
1
6
8
7
0
7
.
5
1
1
9
3
6
2
2
.
5
3
6
2
4
0
0
3
6
2
4
0
0
.
0
3
6
2
4
0
0
3
6
2
4
0
0
1
9
6
6
1
6
9
2
5
2
5
8
8
3
.
0
2
5
2
5
8
8
3
.
0
2
5
2
5
8
8
3
.
0
1
8
4
8
0
8
4
1
9
1
3
0
8
7
.
6
1
9
1
3
0
8
7
.
6
1
9
1
3
0
8
7
.
6
1
4
4
9
5
7
0
2
1
5
8
2
0
5
.
8
2
1
5
8
2
0
5
.
8
2
1
5
8
2
0
5
.
8
9
2
3
0
4
9
5
8
6
8
7
5
.
7
6
3
6
7
0
5
.
8
6
3
6
7
0
5
.
8
2
1
1
9
5
9
8
2
2
8
0
7
6
4
.
8
2
2
8
0
7
6
4
.
8
2
2
8
0
7
6
4
.
8
3
1
3
8
6
7
9
3
1
3
8
6
7
8
.
5
3
1
3
8
6
7
8
.
5
3
1
3
8
6
7
8
.
5
M
A
PE
2
4
.
6
0
3
2
3
.
8
5
8
2
3
.
7
7
2
4.
CO
NCLU
SI
O
N
Fra
ctal
in
ter
p
o
latio
n
ca
lcu
la
tio
n
s
,
ap
p
ly
in
g
th
e
co
n
ce
p
t
o
f
b
u
ild
in
g
Sier
p
in
s
k
i
tr
ia
n
g
les,
ar
e
g
en
er
ally
c
o
n
d
u
cted
b
y
tr
an
s
f
o
r
m
in
g
th
e
in
itial
tr
ian
g
le
in
to
th
r
ee
n
ew
tr
ian
g
les.
T
h
e
s
ize
o
f
ea
ch
n
ew
tr
ian
g
le
is
h
alf
th
at
o
f
t
h
e
p
r
e
v
io
u
s
o
n
e
,
with
a
tr
a
n
s
la
tio
n
o
f
th
e
h
o
r
izo
n
tal
an
d
v
er
tical
ax
es
b
y
h
alf
a
u
n
it
d
is
tan
ce
.
T
h
e
in
ter
p
o
latio
n
r
es
u
lts
m
an
if
est as
p
air
s
o
f
p
o
in
ts
.
I
n
th
e
d
is
cu
s
s
io
n
o
f
th
is
p
ap
er
,
th
e
in
ter
p
o
latio
n
r
esu
lts
r
ep
r
esen
t
d
em
an
d
ap
p
r
o
ac
h
v
al
u
es
b
ased
o
n
r
ice
p
r
ices.
Fro
m
th
e
r
esu
lts
an
d
d
i
s
cu
s
s
io
n
,
it
ca
n
b
e
in
f
er
r
ed
th
at
th
e
s
elec
tio
n
o
f
in
itial
co
n
d
itio
n
s
im
p
ac
ts
th
e
i
n
ter
p
o
latio
n
o
u
tco
m
es.
T
h
e
n
u
m
b
er
o
f
tr
ian
g
les
g
en
er
ated
f
o
r
ea
ch
iter
atio
n
is
3
,
wh
ile
th
e
n
u
m
b
er
o
f
in
ter
p
o
lated
v
alu
es
is
3
+
1
wh
er
e
is
th
e
n
u
m
b
er
o
f
iter
atio
n
s
.
I
n
th
is
s
tu
d
y
,
th
e
lev
el
o
f
ac
cu
r
ac
y
was
ass
ess
ed
u
s
in
g
MA
PE.
Acc
o
r
d
in
g
to
th
e
d
ata
p
r
esen
ted
i
n
th
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
s
ec
t
io
n
,
th
e
MA
PE
v
alu
es
f
o
r
I
ter
atio
n
s
6
t
o
9
wer
e
2
4
.
6
0
3
%,
2
4
.
6
0
3
%,
2
3
.
8
5
8
%,
an
d
2
3
.
7
7
2
%,
r
esp
ec
tiv
ely
.
A
d
ec
r
ea
s
e
in
th
e
MA
PE
v
a
lu
e
in
d
icate
s
an
im
p
r
o
v
em
en
t
in
t
h
e
ac
cu
r
ac
y
o
f
th
e
in
ter
p
o
latio
n
r
esu
lts
.
Ho
wev
er
,
th
e
lev
el
o
f
ac
cu
r
ac
y
o
b
tain
ed
s
till
r
eq
u
ir
es
en
h
an
ce
m
en
t.
Utilizin
g
th
e
Sier
p
in
s
k
i
tr
ian
g
le
e
n
s
u
r
es
t
h
at
th
e
f
o
r
m
ed
tr
ian
g
le
co
n
s
is
ten
tly
d
is
r
eg
ar
d
s
th
e
m
id
d
le
p
ar
t,
p
o
s
s
i
b
ly
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
I
mp
r
o
ve
fr
a
cta
l in
terp
o
la
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52
In
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J
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Sci
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Vo
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3
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3
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Dec
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20
24
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riwij
a
y
a
Un
i
v
e
rsity
,
S
o
u
t
h
S
u
m
a
tera
,
In
d
o
n
e
sia
in
2
0
0
5
a
n
d
a
M
a
ste
r
o
f
S
c
ien
c
e
(M
.
S
c
)
in
Un
iv
e
rsitas
G
a
d
jah
M
a
d
a
.
S
h
e
is
a
lec
tu
re
r
in
th
e
M
a
th
e
m
a
ti
c
s
D
e
p
a
rtme
n
t,
F
a
c
u
lt
y
o
f
M
a
th
e
m
a
ti
c
s
a
n
d
Na
tu
ra
l
S
c
ien
c
e
s
(M
IP
A)
a
t
S
riwij
a
y
a
U
n
iv
e
rsi
ty
,
P
a
lem
b
a
n
g
,
In
d
o
n
e
sia
.
He
r
a
re
a
s
o
f
e
x
p
e
rti
se
a
re
n
u
m
e
r
ica
l
a
n
a
ly
sis
a
n
d
fu
z
z
y
i
n
v
e
n
to
r
y
.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
e
k
a
_
su
sa
n
ti
@m
ip
a
.
u
n
sri.
a
c
.
id
.
Fi
tr
i
Ma
y
a
Pu
spi
t
a
re
c
e
iv
e
d
h
e
r
S
.
S
i
d
e
g
re
e
i
n
M
a
th
e
m
a
ti
c
s
fro
m
S
riwij
a
y
a
Un
i
v
e
rsity
,
S
o
u
t
h
S
u
m
a
tera
,
In
d
o
n
e
sia
i
n
1
9
9
7
.
Th
e
n
sh
e
re
c
e
iv
e
d
h
e
r
M
.
S
c
in
M
a
th
e
m
a
ti
c
s
fro
m
Cu
rti
n
U
n
iv
e
r
sity
o
f
Tec
h
n
o
l
o
g
y
(CUT)
Wes
t
e
rn
Au
stra
li
a
in
2
0
0
4
.
S
h
e
re
c
e
iv
e
d
h
e
r
P
h
.
D
.
i
n
S
c
ien
c
e
a
n
d
Tec
h
n
o
l
o
g
y
in
2
0
1
5
fr
o
m
Un
i
v
e
rsiti
S
a
in
s
Isla
m
M
a
lay
sia
.
S
h
e
h
a
s
b
e
e
n
a
M
a
th
e
m
a
ti
c
s
De
p
a
rtme
n
t
m
e
m
b
e
r
a
t
F
a
c
u
lt
y
o
f
m
a
th
e
m
a
ti
c
s
a
n
d
Na
tu
ra
l
S
c
ien
c
e
s
a
t
S
riwij
a
y
a
Un
iv
e
rsity
in
S
o
u
t
h
S
u
m
a
tera
In
d
o
n
e
sia
sin
c
e
1
9
9
8
.
He
r
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
o
p
ti
m
iza
ti
o
n
a
n
d
it
s
a
p
p
l
ica
ti
o
n
s
su
c
h
a
s
v
e
h
icle
ro
u
ti
n
g
p
ro
b
lem
s
a
n
d
Qo
S
p
ricin
g
a
n
d
c
h
a
rg
i
n
g
i
n
t
h
ird
g
e
n
e
ra
ti
o
n
in
tern
et
.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
fit
rima
y
a
p
u
sp
it
a
@u
n
sri
.
a
c
.
id
.
S
iti
S
u
z
li
n
S
u
p
a
d
i
re
c
e
iv
e
d
he
r
B
.
Sc
.
in
M
a
t
h
e
m
a
ti
c
s
fro
m
Un
i
v
e
rsity
o
f
M
a
lay
a
in
2
0
0
1
.
T
h
e
n
s
h
e
re
c
e
iv
e
d
h
e
r
M
.
Sc
.
fr
o
m
Un
iv
e
rsity
o
f
M
a
lay
a
in
2
0
0
4
a
n
d
h
e
r
re
se
a
rc
h
in
tere
st
is
a
p
p
li
e
d
m
a
th
e
m
a
ti
c
s
.
S
h
e
g
o
t
h
e
r
P
h
.
D
.
fro
m
U
n
iv
e
rsit
y
o
f
M
a
lay
a
in
2
0
1
2
a
n
d
h
e
r
re
se
a
rc
h
in
tere
st
is
a
p
p
li
e
d
m
a
th
e
m
a
ti
c
s.
S
h
e
h
a
s
b
e
e
n
a
I
n
stit
u
te
o
f
M
a
th
e
m
a
ti
c
a
l
S
c
ien
c
e
s
a
t
F
a
c
u
lt
y
o
f
S
c
ien
c
e
Un
iv
e
rsit
y
o
f
M
a
lay
a
,
Ku
a
la
Lu
m
p
u
r.
He
r
re
se
a
rc
h
in
tere
st
s
in
c
lu
d
e
o
p
e
ra
ti
o
n
re
se
a
rc
h
(
in
v
e
n
t
o
ry
m
o
d
e
ll
in
g
,
v
e
n
d
o
r
-
b
u
y
e
r
c
o
o
rd
i
n
a
ti
o
n
).
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
su
z
li
n
@u
m
.
e
d
u
.
m
y
.
Ev
i
Yul
iza
o
b
tai
n
e
d
h
e
r
S
.
S
i
.
d
e
g
re
e
in
M
a
t
h
e
m
a
ti
c
s
fro
m
S
riwij
a
y
a
Un
iv
e
rsit
y
,
S
o
u
t
h
S
u
m
a
tera
,
In
d
o
n
e
sia
in
2
0
0
0
.
Th
e
n
sh
e
re
c
e
iv
e
d
h
e
r
M
.
S
i
.
i
n
Un
i
v
e
rsitas
G
a
d
jah
M
a
d
a
in
2
0
0
4
.
S
h
e
re
c
e
iv
e
d
h
e
r
P
h
.
D
.
i
n
M
a
th
e
m
a
ti
c
s
a
n
d
Na
tu
ra
l
S
c
ien
c
e
in
2
0
2
1
fr
o
m
S
riwij
a
y
a
Un
iv
e
rsity
.
S
h
e
h
a
s
b
e
e
n
a
M
a
t
h
e
m
a
ti
c
s
De
p
a
rtme
n
t
m
e
m
b
e
r
a
t
F
a
c
u
lt
y
o
f
m
a
th
e
m
a
ti
c
s
a
n
d
Na
tu
ra
l
S
c
ien
c
e
s
S
riwij
a
y
a
Un
i
v
e
rsity
S
o
u
t
h
S
u
m
a
tera
In
d
o
n
e
sia
sin
c
e
2
0
0
8
.
He
r
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
o
p
ti
m
iza
ti
o
n
,
fo
c
u
ss
in
g
o
n
v
e
h
icle
ro
u
ti
n
g
p
ro
b
lem
s
a
n
d
it
s
v
a
rian
ts.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
e
v
iy
u
li
z
a
@m
ip
a
.
u
n
sri
.
a
c
.
id
.
Re
d
in
a
An
Fa
d
h
il
a
Ch
a
n
i
a
g
o
re
c
e
iv
e
d
a
Ba
c
h
e
lo
r
o
f
S
c
ien
c
e
(S
.
S
i)
d
e
g
re
e
i
n
M
a
th
e
m
a
ti
c
s
fro
m
S
r
iwij
a
y
a
U
n
iv
e
rsit
y
,
S
o
u
th
S
u
m
a
tra,
In
d
o
n
e
sia
,
in
2
0
2
3
.
P
re
se
n
tl
y
,
sh
e
is
p
u
rs
u
in
g
h
e
r
M
a
ste
r'
s
d
e
g
re
e
in
t
h
e
El
e
c
tri
c
a
l
En
g
in
e
e
ri
n
g
a
n
d
C
o
m
p
u
ter
S
c
ien
c
e
De
p
a
rtme
n
t
a
t
th
e
Na
ti
o
n
a
l
Taip
e
i
Un
iv
e
rsity
o
f
Tec
h
n
o
l
o
g
y
.
He
r
re
se
a
rc
h
i
n
tere
sts
in
c
lu
d
e
d
ig
it
a
l
ima
g
e
p
r
o
c
e
ss
in
g
,
c
o
m
p
u
t
e
r
v
isio
n
,
a
n
d
d
a
ta
sc
ien
c
e
.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
t1
1
2
9
9
8
4
0
4
@n
t
u
t.
e
d
u
.
tw.
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