?
? (I)
?2.1 e?
?
ù5 1
? |?é
M]￥ vBB_·a??
bàD V
1ü
%?ùZùKù V
[ü
%v  ?b
(n 1)
n
(n 1)
p3
! v
^ (é￥éD×
 (1 ×
???é)C¨B
,E w?b
Z
n
(n 1)
n
(n 1)
?? n v
s?￥
? ?￥ ? M?μ
1/2-Z
n
= (n 1) Z
n
# Z
n
=1/(2n)V7

n v_·w￥
9  ?1
∑
=
n
k
k
1
2
1
￡
+∞=→+∞→
∑∑
∞
== 11
2
1
2
1
,
H
n
n
k
nk
n
?# v_· V?à ?iù ?B2T

μ? |i
b
? 1
I
1$
ù5 2
?
 |
ü
H/?9
^???
HW?r

) ?a
e
y0 7ú¤
eíEbμB
?
e1
ü
H4*
 ?
Esò?r?
)?
^N |ü"
y0 ?¤
e￥Z_
??í ?io???

y0?B
?
e1
ü
H4 -

Esò?EùN
|
??
é
HW$
3s
? Hq
?$
3s
?DB?XEù5ü? ?73
bL ?
e￥
y
0??
ea ˉ"
e 7a1?
*
1?B
?
eü?4 -íE
b4 -￥
Esò
HWV
7 ?$
? A ?
^???
8
VM?????V
?RíM???B
^￥?##?M??
??3 7 5sòb7N |4 -
 ?
Esò
?r?#M?
H
eX??
=
E?s
òb
± I
?

3s?c

'tL
!$
?
± I5
ù5 3
?
 |t
?L?í??L
^1
 AaB
1W?
? 10sò AaB
1ò?B?úN |è ?EKí
￥ C??ú
e?C
B?
7
e?? 
/￥C` 'v
f ?/5?_
￥9
^? B ? A￥ú
4?? B ? A￥ú
Qt
$ h
Fúù
esB/eyb
A B
C
3s
? ??  ??]
! A? C?
R 31sò B
? C1?
R 30sò I3B?
HWé
1 10sò￥ uW è ? V[V AZ_
?￥ú
R ? C_
H 7
S a￥ 9sò
=?r￥e Zn?5 ?￥ú (1 B 7a A
￥?μKa 1sò?r￥e Z?n?
? A ?￥ú5?b?N Vn ?TN |
? C_?ú￥
HW
^
￥5
e5?
 BZ_ ?￥ú￥à
q1 90% b
ù5 4
? |Bf
1Hy￥Zb?
ü￥1
?
?|0M?Y)?
? 
???è
^?9
!E
P 
1Hy
]
H
1$
L
!
? 1
1 ?? w
? Z￥
1HyéM]
? M?1
￥? w?7yZ￥y
^@é￥
? Z￥yo1μB?¤(1
ü
"
1b
??
¨
D?yüU0ê?
1o?"1￥1"V
U ?
U0ê? ?¨?Z? (U? ?L )￥??
x
B
A
D
C
O
D′
C ′
B ′
A ′
¨ θ(?LD xà￥C? )V
UU0ê?
1o?"1
 ?
^ θ￥f
1?  ?
(
1o? )
?  ?
θ
U?D1
 ?1
,
?Z?
??
?Z? ABCD
? O?è
A,C
?D1
 ?- ~ f(θ)
B,D
?D1
 ?- ~ g(θ)
??
¨
D?yüU0ê?
1o?"1￥1"V
U ?
1
1 ?? w
f(θ),g(θ)
^ ??f
U0 ?iê?
à
 ?o?"1
 ?i θ,f(θ),g(θ)
à
B?1 0
D
ù5
X? f(θ),g(θ)
^ ??f;
 ?i θ f(θ)? g(θ)=0 ;
O g(0)=0 f(0) > 0,
￡
üi θ
0

P f(θ
0
) = g(θ
0
) = 0.
? p3
óB?e?aY?￥￡
üZE
|U0è90
0
?L AC BDoDb
? g(0)=0 f(0) > 0 ? f(π/2)=0,g(π/2)>0.
7 h(θ)= f(θ)–g(θ),5 h(0)>0 h(π/2)<0.
? f,g￥ ???? h1 ??f
, ??f
￥'?
é,Ai θ
0
,
P h(θ
0
)=0,' f(θ
0
) = g(θ
0
),
y1 f(θ)? g(θ)=0,
[ f(θ
0
) = g(θ
0
) = 0.
?
± I
y
￥1o ~ θ f(θ),g(θ)￥ ??
± I
? ?Z?1éZ?02
?$
? ?1
1 o
￥B?s2
?$
?2.2
?sEy

?
t ?
v?{μ
? ?'
?Yè
^é

¨ MV
Uaé
¨ LV
Ua
HW
¨ TV
Uμ
Hμ?

¨  V
Ub 
et ?
￥
? V
[¨?t'
? ?V
U ?
￥

?1 LT
-1
F
￥
?1 LT
-2
 ?￥

?1 MLT
-2
?￥
?1 ML2T
-2
?b
e ?
?
?s￥e ? ?

?￥'?ê?
M
H
T'
&i??M è ?í
é |
I
1?ê ?￥
9??ée z'
T
S=abi??MbN?
T?oμ
?M
]￥
?
é?Fh
 è ?
Dé
^
?
?TFh
￥?tK?B??

K?

T￥ V |S?'B M
T?1 p 
μ￥[ μM]￥
? μ???é￥
T$?1
^,
?
Q,￥b
1D
? pp,34-37
?2.3 ü
?
?′
EZE
Kl=eE

E
? ?ù5￥ ?dè? b#
4[°¤ ?¨

e?
M ?y

HB??11 ?￥Z
E
^ ?¨
é? wL
EsM

-W￥í
G ?1"'f
1"b
Kl=eE
X??
¤?￥ nF

xi,
yi i=1,…,n
L
!y
?
 ? n??`
^s
?
H°L y=ax+b?í
? yi-
(axi+b)=0B??? ?
p?°LZ?
' p?
a b 
P¤?°L1
￥,Kz,V
U
y=ax+b
y
O
(x
i
,y
i
)
x
“Kz,￥/í5
?
μ
??°L￥Kí  ?Kl
? dL?ù5
?
μ
??°L￥Kí  ?
üZK
l
? L?ù5
∑
=
+?
n
i
ii
baxy
1
2
)]([
Kl
lù5￥3
? ?l′ p3ZE V¤
=

=
∑
∑
=
=
xayb
xx
yyxx
a
n
i
i
n
i
ii
KK
K
KK
1
2
1
)(
))((
?
sY1 x
i
y
i
￥
ü (′
x
y
L?ù5
? ?Ty
?
M
W￥1"idL?
1"7
^ 
e ??￥f
5 VT M

9D
P-1L?1"¨ ?
ZE
E
è 1
×?￥1?
? ×
^B?B? |?
Aí￥?
s??×
)μ
??1￥1 ×Z
E W b V?ó
? 1977
M
?1???×
)￥
W?@
c
×
W?:
c

255200110[

237.5185110
22118090
207.517082.5
195157.575
180141.567.5
161.513060
151120.556
14110952
W 
à 
à
?
×
)
K8
×
ù5
? A ???8×v
e
 ￥×
9
v? ×???8×??
^8"1"
￥?]
)??￥?? ?1?a
;$??
^ ?
3 ?Hqa? ?y
í??
ùM1y
í
]T¨￥2T1y ?ú ?￥
?à
CíE÷?b?á
ì?μv
￥
1 ×?@
c? ?t
?^ V[y ?B
tü
?b1e? ná
ì?^ |V?￥
1 èb
? 1
L?
?
|
°?US"? V[?C??D8
í
@L?1"oμ 110à)μ? è?

[??A¤??b?¨ -
?
￥ZE V pí
1 "
T L=kB+C ? B18× L1 ×?b
FTm
H Là V[b  50à52à)y1
àμ÷ ^)Y￥1 × 89
=ó]D
ì1- ?
??b
? 2
af
?
L?
?i?¤?<W￥¤
s1?é2T

X?￥1 ?
n5
^
af
?'
7 L=kB
a
N
T
|
¤ ? lnL=lnk+a lnBb|e
S
9 |
ù5'
L?
? V¨Kl=eE p
?
b+
E
M -?S1: §?¨￥1? ×?
a
 ￥ Austin
T  L￡=L/B
3/4
ü
^¨?BZE p
¤￥b
? 3
ü?
?
ü?
?
^?
3 ?D?￥X?2T1 è1"w? ?￥

T??
a
i?
?ü
Tb1y ?
D
?5
4 ?/BtL
!
(1) ×??1?ê
m ?￥
ü (?
 A' L=k A
(2)A?1?
&ú l￥
üZ' A=k
2
l
2
(3)8×?1?
&ú l￥ ?QZ ' B=k
3
l
3
1
?

L
! V¤
3
2
3
2
3
21
)( KB
k
B
kkL ==
A ? Kv5?z# V¨ ?1?ê
m
1 ×?￥a
b
3
2
=
′
LBL
3
2
321
= kkkK
? 4
O’ Carroll
T
ü
T￥?1G
^1 è1" L
!HqdèY? V
??vy7v
| a1
?
7 |??b 1967
M O’
Carroll??tDd9s¤
B?C$<W
P¨￥

Tb O’ Carroll
?￥L
!Hq
^
(1) L=k
1
A
a
,a<1
(2) A=k
2
lb,b<2
(3) B-B
o
=k
3
l
3
L
! (1)a(2)
^3
éD?￥d9
pL
! 
3? O’
Carroll|8×s?
?s B=B
0
+B
1
 B
0
1d ?×
b
#μ



?= BkL
? ?HL
! V ¤ L=k(B-B
0
)
&
,k & 1
?è




<=
ab
β
N?? d92T
e ¤ B
0
?35à


≈β
kv?zby7yp
? ￥vl
?1 ?ê
m?￥a
b




=
′
BLL
? 5
Vorobyev
T
?
^B? -
ê ó
P¨￥
Tby
? a1 ×ê
m  ￥?
;
^×t94ú
1-￥×?#   ￥9×
1
L+B V[ A
e
ì÷×
j￥
^y? ?￥? ?b?¨
D
? 4 ?
￥ZE¤
?
￥vl1??a
￥ypb
60)/900]
+
=
′
BB
BL
L
<


T μò?M]￥íEMo1?b1

P
T 
μ V1?31
T
T) ?b è ?á
ì V[1 pò
T
(
@ B=75à
Hμ L’=L5

ò
T1

1 Austin
T

2 ü?
T

3 O’ Carroll
T

4 Vorobyev
T



=
′
B
LL



=
′
B
LL




=
′
B
LL





+
=
′
BB
BL
L
|
T
1 —
4¨ ?1? 1976
Mí￥ ?ò

T??)Y3 +?￥a

? ?V
U1?2T
?1Bá è ? - ?
￥ |E
^? ?Bá￥ 
e
?
￥μs9?1±lb
138.5(8)141.9(7)135.6(7)131.8(8)175110
150.3(2)152.9(2)150.5(2)148.3(2)17090
152.1(1)153.5(1)152.2(1)151.3(1)162.542.5
145.0(6)145.0(5)145.0(3)145.0(6)14575
145.8(5)144.7(6)144.8(5)146.1(5)13567.5
147.7(3)146.2(3)145.0(3)147.8(3)12560
146.6(4)145.7(4)142.8(6)146.3(4)117.556
138.8(7)139.7(8)134.0(8)138.2(7)10552
Vorobyev
O’
Carroll
ü?
T
Austin
 ?
(à )
8×
(à )
è 2.8×D
&ú￥1"
á
ì?y ?B? 8× D
&ú -W￥1"
T?
4 A
?-W￥1"?^YV
 ?￥s¤?^ V[? | d9
ZE ¨
?
ED
L= f ??1
M?￥ü
Tb 1Ná
ì5TBI
"?°?


E???]ú￥ |
￥8×
?
 /V"
Hòú
￥ |?3ü
a?Gê;?1
t
9
?1
t
tb
8×D
&ú

75665954518× w
à
1.851.781.711.671.63
&ú h
ü
50484135278× w
à
1.601.551.511.351.26
&ú h
ü
20171512108× w
à
1.121.080.960.860.75
&ú h
ü
p3
? |V?￥
? h-w
ü

F?C?t
s?¤í
B ·
wL b1N  h w
( |

7 x=lnh y=lnw|
xi yi
? x-y
ü
? ?
i=1,…,15?Q
F?
C?t?+üs?BH°L?í
7N°
L￥ Z?1 y=ax+b¨Kl=eE p ¤
a?2.3,b?2.82# V | y=2.32x+2.84'
lnw=2.32lnh+2.84#μ w=17.1h
2.32
?′ZE
? A?üV
?
? Lagrange?′ E
? Newton?′E
? Spline?′E
? Radial Basis Function?′E
? …
[?T<
? pp,50
? 3,4,8,26,27,28
T<
? Kl=eE p3
? pp,51,11,12,13,14,15,19,20
? I?¨
Dy 
? Submit deadline:
? Sep,20 (next Tuesday)
Q&A