Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://num-meth.srcc.msu.ru/english/zhurnal/tom_2001/pdf/art3_1.pdf Äàòà èçìåíåíèÿ: Mon Dec 16 17:35:34 2002 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 23:23:56 2012 Êîäèðîâêà:

nxq "è | v ls| xv

|llv y ¸k V¦ v y "k m E B@

n i sk ï r v si v "7 y q si v õ qxy ¯ ·

k w n l n i ¸n z n ñ s7 h 7 "ÿ 7 z Hv g) `ð `ÿ u m i q V} 1r { i s | "q m v | l v 1 { Tw r v l s | "q m k w î 7 í 7 V é ì ë ê ¨ V é 5 9 B ² ² 18 C 13 " o "k l r q "x u k w y n i l "k su x2 "7 | 1 g m m v m l i Hv r v l q v y n y k x q t 1r { i i q w m "l u k x l n y r v ¯ 7 `E ¿ @ · E ©@ ãá m l n i "k u z q "k | n t z q l E 9@ ° ¯ ± ¬½ á á qv f °þ f ö áà ½ » ¬ E ôá á f ¯ q "x v Qw Tw o l m q o | w "k m l x "q u t å ¿ ¾ 5 j½ z ± ® « ¼E ®@ ° ¸» ¬ E i v ²ff ä åá » i q i w "k u q n i f þ @ ö å á ä á n y k s sl q m q ½² ¯ µ áà 5 á

Aw n xt E 9 V@ o u v s u 1k h

Tl r n i u ¸q z n i w "k Qu "k Qi y n | "k i `k 1r { i m "q u l v Tx n y q k

E ²@

¯ xº ® « ¹ ² µ « 5 X¸ f · ¶ n w z T o ny 5 `@ "k i | ¸ qi j° T¯ x w "n g sk "n "k v A m "k "k Tx o iw {i "k y | "k i k ni 1x u kx xk u Eovy kyn| k s "l ¥ A o "k i ¸q z w uq "k i 5 x z i Ak B T¸ vi n @ Tµ yn u Ay | n q "k yn | "k im "q u o "k i k i l m vi nv ni Qn "k qi 1z { }i "k Au xi E w "k u iu 1 o 5 V@ A ¸q z T vi o n ni r sv q viq yni x An p | n Qt i w "k u i k Ax olq wm qwmn o0 v i sq o0 o|wo lm | q | sq p

"x v xn "´ g7 t v } i v u Vt 1r { i i n v } "k v u k Qw s m 7E "q `u v m r "k Ti o l m q "q u m ¨ z n "k u n z E5@

Vw m kwn 5@ sv p 7¥

q ¸q s| xv ² T¸ "k

z Av nt E B@ xq| in

o l Av Al ll

viq n ¸v ol k

i w "k u si ¸n xz zoviq mqu A§ o v ±E ®@

ik iq 1z u Q "k Q n « ¬«

i v ¸v n u ¬®

sq "q u { Vi ¸i ¸z Ax i "k v

qi 1~ { i k i n | 7 | s i x

ni An o z T i u v 1z i t

v

q i m "k

n

l

u

ovi l u l i n z t i o

w

1u | "n

v w m o

1~ ¸z xk 1~ m 1q o k

v "k { v "n u z z { { | ~ vi

v| tl "k u u "n i ¸ ¸q Vz q

"k z "k "k y "n vm mn q| z o i w "k

g "k 1~ q { n nq "k yn w u l k "l l w {i

u } q u x v m kw u

"k x o u n t "7 x "n m ¸q xz 1q { i i n v } "k u "q m ¨ z "q k i n x "k ¸q l sw l mn "n k "k 7 ¸9 `¸ A { | y "n t sq Tt u qx 4w ¡ n "n A ¸v u t l 1¢ s| ii xt n n s~ { "l ~ t " o mik 1z { x "n 1 wm i g m u m s ` T i m ql l u n 1q qk "k | "k mq k| 1z 1q ¸o z Ql q "k u n u 1~ iik 1q x q Ai z "k } i "q n m "k { w ¸v v "k v vq { q| "q q sq |w kv u "n ) "k "k "n 1 t u i u vi { "k ¸{ z ~ i u q q xt i w q | i ¸ q o vx 7 "q 1i v p "k m ¥ u "x v ¸{ ¥ © `¸ m { u ¡ o "n l x u ¤ v Ql v Ax o m l k n 5 ~ y " l

|m| l

q mxu i v m u u { v oqw v x "k

n y "n ¢rv 1m "q u llq t x "q Qi 1~ "l u "k i v | `v nii k 1| q ¢ "k x "n v y n ¸i ov m q k 1w

u qvi i u V z st "k nyn u kxm | w "k m ~ xk z Tx sv "k `m x "k u | n 1t A o "k m {ii rvi v x g i An r

"n q ¸q } "n t {i s h7 } nv vi v ¸q Qz 1 1 {

m w i w "k vu u Qt zq iq n t E g7 u v| }v qi xv z 1q n Tw lvt

l s 1~ ¦ { Qw i q q | vi

w i x q ¸{ "q v "k { q Qv | l w n w q

"k u s| n~ Q Qz ut m l ii v "q m v ` "k u 1~ | w To

qn v} n t o | Ax mq rv u t § g um "k m " |l ~ {im ~v

i s | "k v i "q u q 1 nyni ¸ z n i "k t k iq|lv 1~ { i u v l r x q | ¸z u 1t "k si l "n u x{ h g ¸q z v v "k Am o i y xk qv n 1 i v l

} ik i x 1 "n z o tn " u v z xv

i v Ax k "n { m Q@ "k l m Qw ¢ Qt i "n u

"q u Tx s w "n u n w "k u ov uy ~ "k w sq m Q 1~

q 1~ m u y ~v n i "n o v v "n m "q q

1 { ln v n k k u i m "k su | {i

sx qw v m kx Qm l v 1w q w u ¸v v ¸q v u lv xk "q m | v |

v ii iw t "k q s| "n Qt q z q z ms qv ` q v

qni n i 1 m q k " o o v "k m xk z viq ¸z z "k ikw t { m "q u n xk Az "q Vu lqv iqi "k Au

iq { 1 v u "q i u n x "n "q o 1~ m "k u r

w i "q n m xk ¸q z y "n s| m 1m "k i { v m q|q q q xk t

u n z v u n ¸q q s i | "k l "n x "k qs

1 | q v o| Qt t l 1q i "q "q qw i Vk u ¸n Qz

{ Vx u "k Qu sx m q 1 Av { u v m v t l "k n

m

zv kxk uml "n Vm nyq "n m "k { o Vi o iq| ¸n z l v 1 qv r sk gu g u |lv m T ik u j sq

u T i r sq l sw q | n l lv ll x{ |n ¸q 1 q

mz {w ¸n q x "k i ¨ "k 1~ nq | ¸ m 1q "k " o 7 x g7 u s } xk s vi m

¸n 1~ z st 1t v x Qu h g A E 7 zv sn

l ¸k q "k "n u l "7 w {i iq zn vm ii "k s 1¢ { iq Tm v t "k i | 1n

ª Q § q l k i "k "k iq q "n

|n "q w "n u "k v l m ¸q |n v @ ¸v z

7 "k m ¸v z k w m l x "q u Al n l { m n "k Hu ¸{ z q v u Vt o l m k x l 7 " A B 7 `C ` A "k m jl r n i i "k m n "k u "k ¸u g r v i q i w "k u j 1~ { i s | "k v } i "q u q 1 v jx 1~ { i i q w n i 1 { n o | x k w n x "n m ¸q Qz 1~ { i i n v } "k u "q m Tv v v } "k u m l i ¸n z q Qx o | jx ¸{ ¸z z "k u y "n u t q v i k l v t n n i q x q w v u gf V VS f VG Qf Te W V pw 4 V Qf Tc Ab VW Ag Ab XR Ay TW AR 1W d 4 Q e TG W V hU Tg Tg VS f `G Ty xw Td pS Ag Ab XR Tv q `u t sr Hq pi e d VS VS f W ` " T V f G G I VG TU VW ¸a G ha

Qt n y "k t z q 1~ { w m "k m

"n v q "k Al r P

vv wn o p o "n

z | sq l "k

vik ntlv "q u ji h

A e Q Y G V TS XR 4 V Vf f QG Ae `P Vf U Ae VP QR QP I HG F 4 V Vf Af `P VS Tg VS Tf QW Ae P d Tc Qb `P a `Y XS VW ED

Q A T W VU TS 73CB

G VI S QR QP I HG F A@ 9 8 7 6 5 43 2 10 )

(

$ ¸# ' # & % % $ # ¨ ¤ ! "¤ ! ¤ ¡ § ¨ ¸¨ ¡ © ¦ ¨ § ¤ ¦ ¥ ¤ ¸¢ ¡


7 ©5

p q

9§ p ¤¸¦ c ¨ nc Ub r c C r p w nc b p w nc b ¥ ¤7 r P5 vr "f ¢ U tr q x p g D R V "3 ) 9Y 0 @ ) 3 F B V Y u 7 ¡ 5 w1 7 5 F 1 "0 A B @ V 4 Y UV 4 A B ¤V D 4 @ V I XB 4 2 0 1 V @ 3 F B B 4 F w nc b 3 F ¤E D 2G32 FVYB 24@ | {|| 4 3 "0 "V 2 3 `V A "0 ) R V ) 4 F 4 93 3 pw V X B V 2 W nc b G 3 A3 ¤V ¤D 2 ¤3 u t 2 ¤3 7 tD t E @ 3 F yB D08 w f5 4 p 2 3 F E @ ¤V V 9Y nc 21 mD V wb 3 "0 ) yY VQ 42 9E W PA V2 3S "V A H 2 3 "0 2 B ¤3 R H S E F E 98 4 4 x 0 B wD 2 F V @

y ` 4 4 Q ) 3 2 0 F "0 2 V 4 x T 2 PE 3 4 2 3 2 ¤3 D 8 v4 D 4 F B 4 PS H 1 H C p c q C r p p w nc b x p w nc b 7 5

3 "@ G "0 2 G 4 2 0 1 V 8 "0 ) ) E @ 3 x "V ) CY G V 2 2 0 B c x n b ¤7 U wr g i5 f p V W x4 }

"u 4 2 3 S "0 2 8 4 4 2 3 S "0 2 P8 V Q "V ) "0 A B V Q 3 V 1 ¤B 8 94 G 3 u "V A B V B du G 3 4 x "0 2 4 ¤R D V 9T G a T 0 F "3 P) 3 Q 90 D V 9@ "0 T "0 2 D "V ) "V A V 9T 1 u 3 4 2 3 2 1 "0 ) PE 3 V 2 2 3 u R V R 9V W A 0 1 V 8 9 H pp r~ qr~ p r~ pp q ~ qq ~ pq ~ p ~ qp ~ pp ~ r f rq r p F3 "3 m) 1 "0 S 3S ¤ r~ p ~p ~ pp p V 4 4 V wB C@ 2 G 7 CD

A3E1ABA31AV G V 1 "0 ) fY 1 4 4 wu `b 4 4 x T 2 PE 7 5

D 4 u t E @ 3 F ¤B C f1 V 2 0 1 "V ) 4 F 7 m5 3 F ¤E D ) V y V mY 4 2 3 2 1 "0 A 3 B31 )3 D 3 V B xT u t 34 2 PE U 423S E@ 23 G "0 2 3 F yB f1 S "0 2 y8 V2A X8 8 "3

¤E ) 3 7 4 AB V) 3 n `b

D ) mE 5 "V QE 84 Sc

B 2 3 2 7 T 4 G4

32 X5 "0 XT 23 2

4 4 H@ S "V n

2 "V

"@ G 3 fe 0 @ "V A ¤3 W A 4 2 S "V A E u ) E 4 2 3 "3 m) 4 2 3 2 1 "0 ) fE D "3 ) X1 "V XA d1 du "0 2 X8 I 4 u E @ "0 2 8 3 4 2 3 2 p c q U r p p w c r p p pp ppp

4 A B ¤V V 1 "0 ) Y F m@ 3 4 2 3 "3 f) 4 x "0 ) "3 "3 ) mY 8 A E v T b x nc b

D 4 I yB 3 4 "0 m2 3 F B du ) 2 3 4 F R 4 ) G 3 ye @ A Q 90 U ¤E @ tV D 3 A 0 1 "V ) f4 "0 T c p wn b

@V 01 F 3 "@ 4 E V2 W gf

1VF ¤3 D Y 3 "V A D 3 S 4 ) 4A

B 4 V ¤3 u "3 )

yE V S ) "0 2 S "0 D D8 E @ "3 TS 2 3 Y WF u @ I Y) 2 2 y5 "0 V H "0 "3 A

23 A "0 TA 3 )R ) UY "V XA X4 V

1 "0 ) E B V C@ yB V mY ) "V A V D4T A3E1A I42@ 2 ¤V 9D

y4 W T ¤0 B 3B

4 2 T B 34 4@ m2 A ) H Q f D 3AV H 23 B 3 A V 7

)V ¤V D 0Q W E 1 fB 1 5 3

3 @ 1 "0 90 V PI 42

1 VIR "V ) PR ¤E 9B 7 2 321

D V 3 ¤Y ¤1 3 5 F "0 ¤)

V8 7 7g u 4 B4 (

E T "3 A A B "0 S PS H 1

D 3 "@ G "0 w2 7 y5 8 4

i 7 5

p vg

p r g

} tf h g| r {|| nj ¤3 D 3 F P3 r~ qr qq 2 V Q "0 4 9@ 3 B m1 "V A S "u 0 Q 0 F V Y @ "3 ) } {| vf v 3@Q 3 2 " d V 4 ) "D u 3 3FB VT D 4 A ) ¤3 A "V "3 D "3 ) fpw HA2 ppp pp pp

"@ 4 X1 A 3 ¤3 D ¤4 7 6 d5 ¤H D "3 A B 4 9B "0 x 4 ) A w0 9D "0 2 W F "0 2 V Q "0 4 @ I "3 ) yA "V A S "u 0 P1 H A 4 ¤S ( D 3 "@ G "0 ¤2 p rq ~ r p ~ 7 f5 pp pp ppp 8 4 P3 H 1 3 p p ~ qp ~ u q p ~ ¤p j p m v x n j z p m v vr F E 2 3 v2 H x 4 ) A w0 vD rr~ } fz i p p | {|| H 2 W F "0 ~ pr~ ~ pq~ | pp ~ |

7 5 Pi k f n j `z yx p w n j v G 4 2 3 2 1 "0 ) tE "V A wu s 7 nr o "i p p p i qn o i p n o i5 9f n Xj 4 F B 3 " 4 2 3 2 1 "0 ) 9E V Q a 9l 8 m4 B A 4 @ 4 4 2 3 2 S "V A E D V 2 W F "3 A 0 1 V @ 3 F B V fY U1 A 4 "V A B V `B k `f Xj ih ¤H D "3 A B PI H P3 H a ¤3 D 42 a 3 `Y 22 2S P3 3 9@ PI V4x 4 F 8 "0 ¤H D VI H2A "0 ) ¤) ) "0 B3 "3 A Y 9 2 18 4 V H@ F 4 3 X2 TW D "3 "V A ¤3 d G V F AB 9D V 2W "V dA 4 P3 2W F D CB PI H2 F "0 "3 A 4 34 H W 2V B 2 2W F "3 Q V2 "3 ) F A "0 4 A A ¤V "0 2 V 4FB @I CV G D Q 4 PS "3 ) 4 B B "0 "0 4 @ H 1 A 232 U) ) H A3 ) I "3 P3 B 1 "0 ¤B D 3 1 A 4 223 B F 0 F 1 UE I 4 4S 2 3 4S ¤H TB3 4 "3 V D "3 S 2 "0 C) QV A 4 "0 ) ¤2 B4 ) Q dV F D yB R3 C@ "3 "0 92 4 D H "0 A "0 4 ) ¤H D VI 4 B d ¤H P3 H2 x Q F C0

AB "0 42 4x "3 A 22 V A PI H

4 B A 2V 3 X) 0F V `) 3 28 R "0 "0 ) 3 24 2

8 f4 23 "3 BT0 R "0 S "0 )8 w0 vD D G3

BA3 ¤Y D V F3 "3 9) 0 GV2 "0 2 @ "3 G4 S 4 ) Y CF ¤E

F 3 @ "3 ) mT a `l "@ 3 e @ @ A ¤3 D 2 h@ d ¤Y 9u H 2 2 1 "0 ) 7 tg sr AB4 G "V 0 ) 3 u D "3

Y 9V D3 "V A f4 @ "V vE q CB A

3 S4 ¤3 F A ¤3 ¤H ip 3

D D p 0@

2 3 Y "u C "@ G 3 H @ "V P3 ¤H "3 A B 4 p i hg 0 98

4F 42 V e A ¤3 D B Pf 7 6 5

R 4 ) 9Y 3 "3 f) 2AB31 0 @ "V A ¤3 D P3 H ) wY GV22 e 95 dc 342

3 A 8 4 D 22 ¤ 0 @ Ub PI 32

u 32 T 90 1V 4 4 H 1 "0 ¤)

tE@ V ¤Y D g @ "V A x "0 ) "3 H@ 2 3 2 2 ¤3 (

$ ¤# ' # & % % $ # © ¥ ! ¡ "¥ ! ¥ ¢ ¨ © ¤© ¢ § © ¨ ¥ § ¦ ¥ ¤¸ ¢ ¡


D E G "F 9 I

1 "E D T 9@S T20 VEG2 "E D 2 R2EW E9u

5C

c 3 x A 0 9 "F D Qv y E 9 D E W S XV y E Y9 0 9 R S ` S v F di ` x 9 f 0 9 0 V E Y2 B 2 w R F W 0 f 0 G E W 7 R E V 7 Yk 1 y S 9 9 ¸E ` "E D E T x A 0 9 "F D Qv c ¸ ¡ E G S T ia E 0 9 D E hW 0 ic " E G S T ia E 0 Y9 0 i9 w R 0 W S 9 "F R 2 7 E 9 @ "3 w I 7 D "S R S ¸@ C "F R 9 ¸E ` 7 @ S iV S v E f S "F dD w R 2 "F jf 7 dR @ 0 9 w G S v 7 ¸S ` B D hT y x 9 D 0 R @ 9 7 jT y Y0 P I G V 3 20 S 7 T R D QW S B YS 5C 0 "S "S S w B F 9 | 0 l v 2 w E9 S 0 "F D

0

v S W S v S G "F 0 eV I 0 9 E G W B S T 8@ R E V E W 0 D QT "S R f C m 8l U e I 9 ¸E ` x R @ 9 c 3 ` S @ 0 ~ "F D v S @ w G "S QR w R x X 9 F H R @ E S "S R f C ` 0 R ¸E ` R ¸a 3 c 1 3 2 0 D a Yk 1 h y S 9 9 ¸E ` "E D E T R dS R 0 2 0 W F XH S v "3 W S v R 0 9 G S T S V S V "F Q9 0 f F V F H B 0 9 YE i "E YD 2 2 E A "S D T YE i x XW y x 9 9 F 2 0 T YS S v "S R u B G 53 7 H w G S T 2 0 "C S Y9 ¸S ` ¸7 ` S 9 f "S QR Q@ B 0 9 YE i "E YD S v S 9 9 E G 2 0 Xf 0 0 A F 2 @ F G "E D y S @ ¸0 ` "F "S D "3 w R 2 S 9 f 0 R "F R 2 0 B 2 R E B G W B C s C 4 3 2 0 D "F 9 x 9 9 E G W "F R 2 V "E D T 5C y "E R 2 ¸S ` 3c 0 R 2 ¸S ` 0 2 0 W F H E 0 9 E "S D R 2 S QT Y0 F 2 2 E A "S D T S v S 9 9 S 0 A "F D "E R 0 E v F i ` S V "F @ "F Q9 0 3 c " 3 2 0 D ia 0 0 v D E 9 u E 0 9 E f "F 9 8H y YE P c "s 3 2 0 D da y 0 A "F D "E R Q0 W "S D ¸E ` S Q9 x 9 f 0 G H "F QD B G 8V 0 f F V F 8H y S W E "F D @ y 0

D i p 0 2 3 0 I 9 YE

o V 0 2 D BG

w E R I n F W 0 E 2 i "E

"F 9 @ wR m l H F H D da 9 Qu 0 f D

B "{ 0 "V S k 0 ` 0 y x WS

E 3 x A 0 W 9 "F E @ A 0 W 5C @

9

F 5C G RE YV R "F E 0 0 ~

B "F 9 9 `SW F W "S D x iW w "F 9 S w G "E R ` 9 QF B 0 ~ "F D "E F W S V "F QT 0 0 I "F 9 2SVE R 0 "F f 9 H E 0 @ 9 7 D v E US R dW D 9 0 @ R @ G R "E "F 0A "F 0A@9 2Ef0 A@9 7 5r 0 GS 7

¸E Sv ¸0 R v F G 8v E A E d9 D ¸E 9 Y~ 09

` "E S `0 0 f S9 WS V w G2 F S9 ` ` EG E E "S

9 V y RF S ` w x S 2 09 D

3 0 ¸g F 0 "S 5F 1f F @S E S ¸x 7 H S 5 T YE P F G H0 9 EW 89 8S 0 0 x 5g F 5F ¸f ¸ 9F @F FV V 5F G "E 5 0 5F

a V R G@ H "F G2 `E VH y 9 F F7 R2 R f V R 2 S

Yk "3 | R2V 3 T C "F 3s wGS 34 I7 WR2V QW 0 H d 0vD c{ c c|

GWB "S R S F "E D

5C 0 WR 5C 0 0

Y~ 0A @ Y~ E

E0 F2 09

¸f QD 0 f c

c V "S R ¸E ` A @ 9 7 ~ s

} c y ir s 4 a Q hr "c r Qa 0 f F V F 8H y S W E "F D h@ ` E 0 9 YE i "E iD ` x 9 f "S QR B 2 y YE P I B 3 c 54 3 2 0 D 5r 0 0 A @ 9 7 Q~ ¸B ` 0 5r y 0 A "F D "E R Q0 S G 2 0 f y Y0 P I F V F H 5C D R ¸E ` "F D "F T 5r 0 0 A @ 9 7 ~ B 0 9 E f "F 9 H B 2 R I B G 2 0 f x W x D "S R S @ W 5C @ E f x R 9 ¸E ` 7 v D F w 2 E V H Ya c b Qa 82 0 0 W R 2 R E W R S S Q2 XW 7 D 7 V E A "S D UT I 7 9 9 S 0 A "F D "E R 0 y YE P I 7 H 0 G } t r Y s 4 s "c r a q 3 3 ` S H "F D jS ` Y0 P I 7 V E G Y2 w R E V B G v x XW R E V 7 Q 0 f F V F XH y S W E "F D Q@ y S 9 9 F 8V B 0 9 YE i "E D B G V y s4 } { b s | { u hq e s U z c y dr s 4 5a r ¸ "c r a v

"c r a q 0 0 A @ 9 7 Y~ E 0 9 F V 5F ¸f c 4 0 W R 2 y E V w R 2 S 9 w G "E R F W S V E G 2 S y E 0 v D E 9 Yu 2 E 0 9 YE i "E YD E S 9 f "S UR I Y7 P I ¸E ` 0 R E 9 E09 0 0 0 2

u hq ¸x c 4 a v ¸ c q a wv u "t r s 4 Us ¸ "c q 2 c 4 8a B 0 9 E 9 W "F D Q7 B G 0 f F W S H w G S T 2 0 X2 E 0 9 YE i "E hD ` 0 D R ¸S ` 2 2 "F "D C V "S R ¸E ` y x 9 9 S 0 A F 2 @ F G "E D S v YE P 7 ` "S 0 0 R E R R W EV "F f 7 f 5C 2 ¸S 82 0 7 G S T RBDS `0VS 0vD 22E e4 WS Q2 E9 A "S d v w u W D XT g 4 i R 2 "S ¸S ` y 0 D "3 Xg 0 D S @ X2 ¸7 ` 0 x99S 00 D T " REB 9 ¸0 Q` 0 A "F A B "F G D "E F2 f EV 09 R @F 7G "E 9 0 "C G "E QD 2 F W QV D T iS Qg "S D "S R S9wG yE9 wR D 2 S YT "E R D "F f R ¸E E FWS EW 0 ` "F 09 V 8 G D F EG V "S H "F D YF WSW 2 5C R ¸E "S R 3 ¸x R2 X0 R ` 0 R2 7 R2 B9 ` "E YE P E "F 4 D 0 X2 " 3 "F i 53 y I DHS Qg 00 S9 09 YW 0D AF y E E Q9 T "C 2@ E9 f "F 9 B FG 0 XG H 0v 0A2 "E G ra 8V I "3 0 D 0 ¸7 ` DE D B F w 2 S 9u

RS9

FV 0D E "V @F R2 9 9wG ts

8H y S W E G G "0 E F V "S "E y E Y9 "S @ 2 G SG27 0 9 ¸0 8g I f QD S W ` 5p ih

F R 2 y G D E F rq

"F D C "F R F Q` ¸7 0D

8@ D ¸E ¸E X` 09 22 QS y ` T "S

p ` ¸7 E S ¸S ` R

l l 0 2 V ¸E A YT T "E S9

o D `E "S "S S E f "C

nm QT R D G 7

k "F EWR2 I7 Y` B 2 SvS XS R E D XR @ "V 0 ¸W

R 9S 7

E f 9 E 9 W B ce

@ "F jT ` "F U@ g S D HS D "E 0V 0 7 0 R 2w Qa 2 A "F wG A "F wG R H d

"E R T2 "E R REV S

c b Ua ` E 0 9 E 9 W "F D Y7 X2 0 0 W R 2 R E W R S S Q2 XW 7 D 7 V E A "S D UT I 7 9 9 S 0 A "F D "E R Q0 B F P I 7 H 0 G F "E D "C B 0 A @ 9 87 6 3 54 3 2 10 )
f f iter (N , W , N_Iter , f ) := h ¬ f N 1
i i

(

for k í 0 .. N_Iter - 1

$ ¸# ' # & % % $ # ¨ ¤ ! "¤ ! ¤ ¡ § ¨ ¸¨ ¡ © ¦ ¨ § ¤ ¦ ¥ ¤ ¸¢ ¡

for i í 0 .. N

for i í 1 .. N - 1 r i ¬ f ( x) x ¬ iâ h ¬0 if N_Iter ¹ 0

¬ (1 - W )â f

i

+

W

2

â È(f Ê

i- 1

+f

i+ 1

)

- h âr
2

i

Û Ø


E 1 1 9 d "5 8 AX 5 F 5 @ @ 5 ) d "E 8 "9 7 q) E F qE AP "E 8 ¤9 B 5 v@ 7 Q5 ) ) F 8 9 @ Sr ) 7 1 ¤5 B ) 1 ) D E AR 9 ) @ 9 "5 8 7 1 65 4 "2 u 2 1 0) (
0. 8 0 200 400 j 600 800

E 1 1 9 d "5 8 qX 5 F 5 @ @ 5 ) d "E 8 "9 7 ) 9 F qE tP B 5 qT s "E AI "E Q@ ) ) F 8 9 @ cr W ) @ 9 U "E @ AR W qE 6p i W V 1 ) bU ` D "h W ) d I @ Sg f 2 "e 2 1 0) (
E Ek ¬ e

C ) d "E 8 "9 7 c) ba ` @ Y V "9 7 E D 5 T 9 V 1 5 AX W V QT ) U E T E SR C 5 D 9 "E 8 QI C ) @ 9 P "9 A8 D 5 I H) G "E 8 AF E D 7 1 C ¤9 B 9 A1 9 ) @ 9 "5 8 7 1 65 4 2 "3 2 1 0) (
0 0 0 0. 2 0. 4 yj , z
k

$ ¤# ' # & % % $ # © ¥ ! ¡ "¥ ! ¥ ¢ ¨ © ¤© ¢ § © ¨ ¥ § ¦ ¥ ¤¸ ¢ ¡

iter_e(N , W , N_Iter, f ) := h ¬

iter(N , 1. 5 , 50 , r

iter(N , 1. 5 , 30 , r

iter(N , 1. 5 , 15 , r

iter(N , 1. 5 , 5 , r

F (y

j

)

B

j

)k

)k

)k

)k

0. 2

0. 4

0. 6

0. 6 0. 4 0. 2

Ni := 8 0 0

0

for i í 0.. N

for k í 0.. N_Iter

e¬0

f

r i ¬ f (x)

x ¬ iâh

for i í 1.. N

for i í 1.. N - 1

f

N

e¬e+

1

i

¬0

i

B : = i ter_ e(5 0, 1 , Ni , r

¬ (1 - W )âf

(f

i

-f

2âh

i-1

i

+

)2

W

2

+ hâr iâf

0. 6

)

âf

(

i-1

j := 0 .. Ni

+f

i

0. 8

-9 14

i+1

- h âr
2

1

i

)




I S 6 2

6A "G eS gA r 6 HX

h "G ¸B ¸6 I f

p I g0 E SU

8 H6 r P6 a 6

0 "B 3 A eS

T 0 p I "G U 0 "G

I 6X T `A i

¸6 I @ "6 p F S B 0 h G

p "G A r "G

U HX S S 6 `U X BFBXE PA

g6 r 0 00 0 "6 p 320

X Q U p{

HF i PG I 2 6 X k

h G 0 A `G @2 " 1p

} ¸B B hB

I 0 A p

"B p AB "G g

B FB eA H

HU h XE 0 k B

Bf 0 "6 h AS

F B T g2 6 p U 2 6 X "G p F G X H6 eX 6

R "6 h gB r S gX @ R "6 h

@ T S "G eh G 2h0h @ T W

W k3 "G "G p e3 C

00 U X "B 0

ABT 0 T tS p U "G Q PG I

X "G 0 S 0A

p 0Q T "B nG

U "G "G p p Ph 0

A I 6 h 2 A ¸6 3 ` h2BXE

Ah I 0 0 "6

"G p B F 0Q p

8 6 0 PG I U26

HX `0 S h 2 "6 p 6 S 0 A G @ X gB tr

"G h e2 0A h 1f

I B0 BF x

¸6 A B 3

I @ p U X B A ¸B I E 0 X E 0 "6 p U 3

¸t " 1d e b " t t r 1 n " g t 6 A S Y6 B 6 X 6 R 6 T "G 0 W 3 " 3 2 10 )

S

"G `U m 6

B X 6 ~

" t r 1 n 6 r ¸6 eI 0 I0AG G 2 A "G p h Yi f be d 3 Yi h g I "B 6 fh 6A pB R6 26 AG eU T "G

t gA h B PG Xh hg @ T W

" 0Q E " 2 "G f

g PG I X "6 "6 p HU AS be d ¸6 S 6 ph

e 0A p F gS 66 R t6

"G A nG "G R 6 ¸0 I

P6 I ~ X 6 @0

6 0 ~ S 6 A gB

R6X6 AGFE `4 6 R 2 0 7F R 6 T "G 0 r6T

R 6 T "G 6 e2 F gB } G I B 9 8 nF 6 0 p HU 60Q XE0 6A Ch

0 F "B p rp t6 R6 ¸0 I

X B 3 B6 Ay

G F g6 Y 0R

6 YE "B 2 z 8 fp i



h u6

y X PG I p H g T 6 n8 C `F @ 0

@ T 6 v e h 0A AG E p S 3 "G

" W "3 @ A X E 6 U 2 tm I h r i x g i u e "B PG 0 G 6 Y 8 X6 FX Pj C PG BT X6 0 "6 | I @ Ei G G g A bU T6 g0 h y B T `F

3 6 g2 HE bS U2

¸t iT X g A hB `0 @

e 6 @A p p nU

1d 0 h I 6 0 T

f S R h 6 "G 6 6 X 0 PG I h eB p m Q "6 G Pm l ¸

U A eS h iE 2 B 6 "G 0 T 6 yG sp T q

A

6 @2 h U 0A "t kj P Yi

i hG @T S y "r hg B A h6 BG Y8 Py p

G r "G S h XE6 R6A G p Do f be d A " H2 h yX 3v

A h T w 0 "G fU 0 6 S S S "G

Bf 0 Q PG S 6 eS 6 A

F T P2 2 @ h r "6 x 0A G S x w HS i G "G G `G "3 h ih "6 tw 8

B 0 tw I ¸G nS R eB

" 3 g2 F 8 T S "G r 0 A "G

1d " Y8 y X gF "G A U "G A { P6 v R "6 h 0U h p 6X h U "G 20 R

gU 6 gA r F "G HA i h 2 "6 p 0 tF 0

gI "G "G `S S PS f A X

U 0 T gS "G h " Y3 t g B "F 0

6R @0A Y 1 X I

6AA BFB t 6 A p

PG I 0 "6 p U A ¸B I "B "G 0 A

A eG 26 pB ¸0 `I

@0A HX 0 h `U @ 0 tX h

GF 2 "6 AB BA

6 2 6S "G A 0A U

BT2 `2 6 E 6 R E 6 X 0 T HS

6 AA 6 F B @0

"3 @ "G p r 0 A gB AB

2h0 Y8 y gX "G eS @ T r "G p FBXE

F6 ih F 86 0 "6

XE GX S E 0 p

0 "6 6X 6A B U26

pU h f2 6A `X

26 2h 0 p A "G ih

X BX h p 2 "6

6 6 YX "a 6S

2 F 60 wv

@ B 2 x `2 i h

h f g8 p Pu 0X

BGF 6A "B p B ts f 6A

E6 i HU S "G h

g2 T "B U6 2

6S h w A gf ed

iT GE@ x `S i c

0 p{ h ¸B 4 m k ih nA 6 p P6 "3 6 S `h U 6 B 3 h G r BT6

¸t YI i B p ¸B 0A F "G 3 @6 0T `A 0 "G A gG bU a

" h "G p S20 I0p "G p A 6 3 X `F i S B SX6 S g6 6 q3V 34

"G U 0 T S 6 R 6 A A 6 0 Q PG I 0 A `G @ 0 A G F E 6 `2 @ T `F 6 A S Y6 B 6 X 6 R 6 T "G 0 W 3 "V 3 2 10 )

"G U 0 T S 6 R 6 A A 6 0 Q PG I 0 A HG @ 0 A G F E 6 D2 C 0 A B A 2 @ 9 8 76 5 3 4 3 2 10 )
0 0 iter( N , 1. 5 , FRAME , r ) F (y
j

(

$ ¸# ' # & % % $ # ¨ ¤ ! "¤ ! ¤ ¡ § ¨ ¸¨ ¡ © ¦ ¨ § ¤ ¦ ¥ ¤ ¸¢ ¡

)

k

0. 2

0. 4

0. 6

0. 2

0. 4

yj , z

k

0. 6

0. 8

1


B °



t



"®

¤} { } { ô t} { à t¡ { ¬ t¯ { { z

x ñ ñ 2 ñ2 ð c ) C 6 h "A V @ 6 7 ) U f Y 1 58 j { ÿ ÿ ÿ " T ¨ ï w t{ T 5 ¤ { z B w " { ¶ ± ¤« { {þ{ º º · ¹ T T ± ¸ ± "· T ¸ ¨ 0 § ± { { ¬ "z ª { « ª { ¨ 0 § { ª B¨ © w{ { { "z B w{



å z ¿ ¨ t{

"¾ ¨ 0 §

î T tí ½ B { "z ± ¦

¨¡ g± w{ "z { ± ¥ T 5

ì B ¦ w{ ¤

áë t{ t ¥ T· {

t¡ ½

ã t | 0 T ¶ t ¨ 0

¤ t tõ t ½ ¤ ¤¶ § ¤ 5

5ä ¡ ¨ ¡ t ¤ ° ¥ } ¥

¨ á



¿ "ê ã ã 5 5 å t ä T ± B µ ¤ ¤ t ¤ 0 5 5 "ä B ± 0 0

| t tä 5 t ä · ´ w| 0 5¸ 5

¨ ¢ ¼ ¤¶ ¨ | ¡¢

¡á 5 ö t¢ ¢

}¨é T} ~ á ¹ ² ¢ ¡ 5 T} ~

è T| ® » ¤ ® T } T| {

"y Tv x Tt "w "v u Tt To sr Tq p 0m To "n m t2 tk A) w@ Tu C A VAD A ` "6 C 6 r 6 8DAD y x wv @ U "6 D T2 ) 6 1 C 6 7 "A V A D ) wD w) A D a V A @ @ 8 h "8 Y ¤A wd ) Y 1 ¤8 d ) h 8 a 1 q Y 1 "8 V 8 C 1 "A Y ) D @ "6 BV B d l "6 V Y ¤A d "6 V "6 5U i ) D A ` "6 D r Y 58 6 1 1 A "8 V 5U 8 9 8 D D 8 ) 6 1 C 6 7 "A V ) Y 1 ¤8 d ) h 8 a 1 ) Y 1 "8 V 8 C 51 q Y 1 ¤8 d ) 1 ) @ 6 Br "A Y f h A 7 1 51 "e d T2 ) ) 9 D A ` "6 D Br A 8 D ` "8 tY "A Y ) "h "6 D ) ) ` 6 h 6 r 8 @ A "6 V tC A t s @ 8 D D "A V Y ¤8 d 1 1 "6 5V A ) D A "A 5V A 8 C 1 A ` ) Y ) 7 "6 D t6 "A Y ) ` f 7 58 Tj d 2 d i f f 7 ¤f d V 58 h "A Y ) ` f 7 8 U u d g Tf u d f i ) D A "6 tV s @ i f r q 7 8 U 51 ¤e d x T2 ) ` 6 h 6 r A ) 5 c f h A 7 1 d "6 Y D A h f Y g1 d A 6 9 6 7 h "A V U ¤s d i ) D A "A V 8 9 8 D q 7 "A Y i "8 Y 1 ¤8 d 6 1 i 57 4 T2 ) "6 V "A Y ) a ) 5 c f h A 7 1 8 U i 7 h i ) D A ) 7 ) V U 8 9 8 D q 7 "6 ` "6 D A @ Y 1 i ) D A ` "6 D r ) Y q Y 6 @ 8 r q 7 8 U 1 ) ) A C Y A 1 8 C 7 ¤A d A A 7 8 "6 D A ) D A "A V A 8 D D A ` f 7 8 U q Y 6 @ "8 V ) 7 8 U V "A Y D ) "8 V U d "A Y ) 7 A @ A D ) D A 7 1 ) t` s b@ d A 8 "8 V "8 Y 8 C i 7 "h u A C Y A w1 8 f V 9 8 D q 7 "A Y ) 1 8 D Y 8 "6 D Y A ` 1 "6 V ) Y 1 A @ "8 V U Y A f h A B7 2 52 d "A Y f U d ) C 1 A ` ) V ) ¤U d 8 D A ` f 7 8 wU ) 7 ) y pv ) C 1 A ` ) Y ) 7 "6 D 6 8 q tY s Y A ¤8 td A "8 V "8 Y 8 C Tu ) ) 6 1 C 6 7 "A V "6 V Y ¤A d "6 V "6 U A ) D A ` "6 D 5r A 8 D q 7 B6 d ) Y U 8 q Y 6 @ 8 r q 7 8 U 1 ) ¤8 d ) h 8 a 8 5A 2 T2 ) "6 V "A Y ) 8 7 1 ) 5` A ¤8 d ) h 8 a 8 A wD Y A 6 q D ¤A d f i ) D A ) 7 ) V U 8 9 8 D q 7 "6 ` "6 D 8 9 A "8 V 8 wa V 8 t Bs W 2 x 2 ta s D D A h A @ ) V 0U "u @ "8 Y A @ 8 b1 ta s D r A 7 8 gU 8 C q 7 8 C 1 A pD i 1 Y ) h 8 9 ) V gU Y f 9 ¤8 ed c 7 "A Y "6 Y ) b` a "6 Y A ` 1 "6 bV a ) C 1 A ` ) Y C "6 V XU W T2 ) ) D A 7 @ "6 V TS R "Q 0H P I H G F E 8 D C B8 A 8 @ 8 9 8 7 "6 5) 4 2 "3 2 1 0) (

$ ¤# ' # & % % $ # © ¥ ! ¡ "¥ ! ¥ ¢ ¨ © ¤© ¢ § © ¨ ¥ § ¦ ¥ ¤¸ ¢ ¡