oa NTs _ oe : ” Tntor polddioy Me ha Me a the process a Computing ye PO fol Some vedluves ay a lich Wes blu om trtowal) ic cabled | interpolation + Dy , $eds raptor, we tntioduce eobtal raw cablil tt Sawer , hoceward dtHerences and central differences of a function N= F(x) Pou - Gy ; Fouwand difprrences : tet Ve-t(w) be the functional nelationthip blw 2 Variables X EY ene ts the independent Vortable x and Vis te dependent vontdlble.’ tek x takes Hee Value Ber Rutay <8 | Kn andy gels toutes’ Hat!) Value Vo, ¥,7 yy” wy otw: wh Gh) - Hoo —_O i Here, bts Ae Teubaad’ Ueperence!’ cpesitiey pak x2 % in eang i vy POL) & $00) = Fimothy tems) p's VA Me = Eoug)th, SYo= Hu)- +L) ~. Y= 4buy ®Y0 = Wir de We POR KEK Mvegn@! ” 5 & ton) = fut n)— FO)” yo OY = Bap ry vs Posies sys, = be KAYE Teas 9 cathy Poke OGW Napa a (ntotig OS) Crwand Lheronce table : x Y fay a | ) | aby aty x ; Par i -| e Yee. Ayo er | AE 4 BO 10 aty 7 gis 6 aN 7 ». a 7 ah | s Me DY Pep, | z fee | Rectan lipprence gt ae él ! . fi i. 4= FOS be Hew Functional rdaktonsiip blu & VamableySere th a. Wndapenduntii G24 i RY. hee x bs Tndependunt Voxtabcle and Y 6 indent Vostcusle « i ty! balers tte Volise mor Au Mar cond ¥ tales ste Nabue Yo, ry Ya 1 TE SEIN) i ah) ‘o. ' SHAE TEC AGE Symbol OF Baclevonsidl ayo ape af pub aaa NS BeV/O! > ya cit arty) = ey) EMD A ge jon a7 Tae Qi Yo. ; ie vp A lind fa Rh a Nar Me ORE a eae fasiy tiene’ A eyo) «Oe Fe noe Yan Yn sl me 273-=) eo tfference table OQ as h of yutyeyt ele” AY Oy tery! Bty fe Xo. 1" geet \ va MY wa vy you = of 4 ae ee ee Soy Se /3, (i ai x P % Ie yy v ei Gye WN OY, ag Tp (x) = 4+5K-7 féima table 1 Wand di ” taking x= WO lS, U/S hou Hak tre ee axe omstant J Cs» Jase feats Ts ! [ety [-3 A = Bs aT hes] ee Frwond difterence table . i dy PMA BIAS i at ae Ac Fall 6 ' ‘ if i ° . 2 24 A 0 f ee, ua OAS VAP Cage 4 *the soe table gives Set q Vals Ux, and the Goneypencking value dp Yo #4) x 10 IF as |30 |35. Qrsi Re ee 25:34, teible” Heal. oon coum 20 2247 q oies Gaom forworkd — difference Here Vohlius) a AH) f 20107, O2fU5) jist #(15) : Fonwad Aifferunce table.) .), ; fa) Lag ag” Ie, . 4 Booth tie 4 to | (Site = St ROMS soi Wily Is Bers ly ‘otac S "0-610 0°04 [OBS ! ogee etl.o50 -o0°ol 120 ais 2252 0708 0704 1139 og 0703 0 265° . ZO 2y-65 pud y vs B5 25°84 ad fs) =e 0201, AftUo) = St ( OY £0) = ~0°580 Bt eulsd= oO OF > DB the interval of diferoncing yy uty prove tok ‘A Te Ot G42) (at3)] = te (AEN IC2) OOS) oop oy we kmow trot 5). ettn) = $Obh)= FOO fia) 2 @ (acr2yi(a3) 12 4 Ate) —7® A= + (t+ - lee (= KUATD Heatly = Ket (442), OFS, Jt Substtuling <4! &@ ™ eqn ® B [a (ar (ate) (ut) J = (KEV HD) OD) (aty) - x (att) Cat 2) OLS) = CO) (Kt2) (xt3) [Rte x] a Freire 2) 430) 2Averog “operate he 4 di et the Ha voage cpoator ow dein ey is ECs, he J , | wan lard ‘Shifting apercitior Yeh Saget 4 ar The shifting pbs HEN. is ¢ ‘defined py: theg prvation ‘ry ‘= ac) tess Sous tei the HE te, ey cathe He functtonatt value Yn repr 4 he next higher Vole. Aotia peg vs ql eens P ae fre 4 “| Pee tide he Ein RE ayy eg Seek a e = Yous SS yay fe ae : ; ‘ nie? Yas (or ha i ie B ssloncnse OM wes thee aga" = (Oy we hove} OY a oro vs}j Ha Laveadge! gfe Bo nh oo HTB, ay EW Ey Patt tg Ble tie = Yo [e-1] , i Om 4Tef] 6+ Tet] oy Feat > Relottonrtalp bles blo ee 4 jee BE = Teme ee] Ph AQ) 2g ee know +tak, ' \ ie Jtyn = 1 Cais 1b Yn EU ney = rn] a cme | Tc ot f pa 2 [eM Mn - +P Gn] a ror tNaoktons Fetwand ‘nterpallation founuloy: 1354 Fn = Yor a Og uney Sat YEWOD rg, : u ‘ Ae i ( ahha . 4 VLUDWery Hy? hee &! 2 Meg Oe YOR Pd) Cr pay Pro F here, Wis the Common dR [ference Newtons back wand Snterpotation fimulo’: f= Yast ayy 4 ver or Ju tutta) x ta Ze ae et PE wont Sf AME? Aida tR Some cetie sue Br ae VW) Wha L DS yn ee ye tee COG Hep ai Oe | he common di pence! the population of a fear (in, tte decimal Senses wes gen below: timole tu population fh Hee yer IAS Yeoa LX) ISA AOL ane lap WJ “Pa Pt is populoatig(v) 4e 66 08 93 to} sinte, Ate = 1995 - Ues,.Stankeng . oF table: $0, We COU) | Abe newkors srrvoand water polatten formula i Foye Yot 9 BYot Ul 6G tVWA)W2) 24 lay lee US, Sp t PLOW) a i) N-F-p +able <~ “4 aL By 2 ee ; - , ES wv a at (aq) 4g aa d (401 6L Uipocis) @ i ¥ 7 fe) - 2 Ary & By ee, j ») (Lda) ge) yo "38 aE | a2) 34 ) c a4 1931 10) % + ee©. ke ; =)0%ffh eps Mh hh ie 6 $U895) = 464 O-t; (24) +O) (5) + o ¢(OU-1) a 7) APRS) 8 y I + Ov (OmG—U) (O-Y-2) LO-Y-3) \ sane 4 4 APE PAF A 2 BH 658 vol folly log? ie Fewotns eaexeaond, (Ud Fy? tbe, boo ieg Since xe 1425 tes” : ah 4 use rectors loaceurand _ fnterpolabion total val > i lott) ge oUt) LF Fo= Ynt a Son) ae v Ant =f art cae OLA YB) Saye x ae same able’! ' a Ph ¢ Peay OF Us $025- (93) 2 HOG )) yee (aaa wy KPA ee ee (241 Ge we 1 Mt} 12 Jeg? tau » Ql =3 ink ¢ W243 me 1431 lol cy) Ww ¢: Haye loy4 C0) (9) (0-6) (-o. $ OB Coed) co 0:6) (—o» a 4 BIE ce) nt ea) + 606) Core!) t | : Ho j Coetsy = Wl - &Sto.qg_ 01056 +05 104 oy = 16. 83T-Ty Ho =I » HHO, Moe 5, Hg=22, Mae ST tind HG. Tel? Given eta uh ig ‘ a. | sof s| BM) ae « i fae [1 [o 5 |aal sq Simce ak X= 05 ] 7 i uring, NOPD fmito, ne £00 = Yot Udyor veord Yo a vlorlu2) , Sh Ye 1 Weeds 3 L do) _ Ose oda ahi Rowe wet! 9 NED Table aye lsh ra na ms) eres AY og =~ 2 ed Nob ost ge )oGeank: b9,"A@} obo eoiAtG, 0 me 4 te ° eS a5 \e ; i 4 87 oe Ls Ts FOE at 0:5 (1) ies SY (0, eNusnory Ye 3h 0-5 (0-5-1) (0°S-2YO-5-4) tos) = a Sener (0) FR K=O 23)5 6 L0Q= ld 1S; Se find £03) sg, Newtons forword defference! pete! (O12s Given throaty R20. oilsig® oD BB) : a% V4) 1 1g 1s 6 & Using giSince f ok x 23 Using nh ET sfovmulla, Fad = Yor Vdyo+ vlw-t) Wyo 4 (VA) (0-2) ds & a ot Veo vs U= 3-0 : =< Dd WS) | ae i 5YE Be ee Oe ot 5 \ " \ fe AY sinh: \ \ ts -u al Bee tO ages 2 ! > ‘ | A) | —2 eS By uiteg FT Formule Hays + WSU + ulu-) (OA) (U-2 Yo Yo Ps 8Yo OO 4 o(o-ytory Heuer. 3h (vs) 4 = : ~s, NED table ie eh 0 BON BO AAW eh ramad | oy | 3 z tl 3 | pape] By 2 “*O cw ) =i | ae 1S = Zfind THE Grbic poltpnovntaf odd, falestew « folloutig yobs — Yojrl qr . {A= t, YEW hence our ovr 4 (4) : « © BY > Apply Newtons Onterpolotton formula compute tre value % VES Geven that V5 =2-936, NGF RK49, JT 2 2.646, (Ee 8.898. Correct upto 3 decimal le Y= fay Yee. a! 6 qo yk RAD BWYGY LEGG 2-828" Lagranges Interpolation t#mula An be 4ee? (ney Value oe v Yor dA wa lee Yor PM bas > alidh aw Not necenarly Equally’ § Yn be the Corresponding vou 9 NS etly) Te gaaeut Some mre pcm) (4%). EvoLuiet 50d) gfuen “Ye, Vee, 42, 336 ak AEh 4S respectively. giver lagrorges pirate -tetrnula « a Given feck,” Ne x \ a (S. Yetta) 168, ytaae 336-5 | ae k : «earn, Hea Vous Ao, Med | OMe RES Yh tates Hae! Voli “Mor Mer Ys) By using lagranges tntexpolakion fyimula “Enyce Oy) Ge) & rhe) Oo) yg) ALON Pei) ( 2 ) Yo* (ante) 2) Bo) OW)aa 0 ie to is) " 4 MOE oe (io- Is) Cle uaz) + ° YC I8) G- Duets) SMPs HL B84) Usey Use fuo)= 23) Hind te Unique polynomial, por) % degree 2, leo Sach thak = PLY =I playe 27) plu) = 64 Uring logranges tnterpolation. toxmula, Bee al Bes) Rene ie OI § NAAM. > 0.04 bu fotmetlo, by ey Legaaiges Ge ey : Foy 2 GW" Gey’ peers 5) eye) Cay) © Goi) (e742) a ot eA) Carts ) Cae, =P) wetenerw | (aay wept au) (EY (Ua) trol ) ES eoU KR BK! hy Reap 2a reer 4 tae dia’ —Zx-x143 Ad) B+ (-1) (39) Sings 2 WOK rE ext 4 ‘ i io ae Gat Rwets 1h g # x = XCAMH2 4-8 Spmeacres x KA Xtae —————— > Sherr. Nek AIL gx text 6 Gauss forward tnterpolatton formula : P= Oe dor Vat MOP nee sotoucuny , Baty Y= 1) (¥-2) (Ufa 1 fee We x-%o : ee ee. h Gouss Backwand _Islerpolatin formula » Ge Fs Yor Vay + ty oy E YO-DUED 2 i as 2 Y(V-D(va(Vt) 4 — ait ya ty «I “4 lee UW= *X-%o 5 n ea 7 Find yey qven, derouk YlA) = AY ry (2H) HBS (48) = 35 » yee = 40 Using gauss forwork ditference dibs DI Qiven tok, | By uring — gaun foswond difierence towmnula - Ge HO= Yot UdYo = ony ot NOBLE Dg + VU-) (ODWWtY ge a | ae= 32.945 he ce cae Find #8) given Wak ‘data’ {(25)= 0.2107, (30) = eS 2027 , (35) = 0:3386, ALO) = EME Ghen taal, ey. eg ih Bq uring gauss Bitaads dite faim Y= 400 = Hot Ob qe + oH) he eb Z fat’ 4 3 | a) x K aor x oy ye a ‘1 25 omy 1 ey a a ee My, a ' 0-0830, 4A. Ho 39 6-202%y 0.0039) = oBS4 = ee 0.0854, 5 O3sse —'* od 0.0408 go, OUbom Ma ag) 2a Le woe 3g 5 = ‘i x ; 42 a) =o 3035 + (ods (010854) 40-4 )LO* © Petes) 21 bon BY “BER He Corue foet) | ah gat) = 0302+ to-4) (or 0320) + (04) 4H) (0-089) ype "Wis Gl igs Sh Pula tot Dy ae ak =OZlec: he Find $230) fim Here Follausing) toile: YMC GLE 0 ag “gg Me Yo 95 FOS 1-39 9.03 tar B46 by uring, Gauss Backward diHerehde! \yindla’ Given tak, Fy) * aie “ Is By uvtng gauss Rackwand. ditt forritile. ule mW oq ‘ q a> BC yA 7 8605 id he yw 4 4.03 fs yet Od ' yold-46- \ v+tt i Hy = Yor veg +t Oey 4 Uw EAD y PA | BI _ boy Say PLUFDLU-RLVALYY f a bss dl i oe Paty LWA) W-2)WW-32)UHY s “1 a Fe Ag Ve 236-23, { y a at ——t = FB og. . OdFLY) = N02 +f Co.2)(1-99) + COR ORD ous ye \ wh LOR G2RCP2-2) (e241) ic Ve we ) (6) + le ced © Gos {ca2h ~N(-0-2) Coa-s) 0a ty “Weary 20 5% 30 as) uo us... Gams forwand -) i : “T3S4 Bar vay 2e0 23) 204 yuank Bee) yh a> qe 6 Wd 7 ne. Wo-ZT i : 2 th zm Po “1 O84, : ( FLY) = Yo U4 Yo SRL FD £9 2-QUB (ay al =A =) ay, | LLY) (U-3y LUE) May 2602) aD 0- -4)tW41) oo Sh ey ee og a = petenotan stoi eo (0-6) 00-1) (o> etl) ol. Sa gar ee a CO} iy aq fr 4 + 6) bo, eee?) em ‘oa eee. a igs) * eo a | Stealing 's Leimudar ayy ie. bea 4 es x f Poe “AL Cee GE O08 1 ale eG ee a Reel] Bo | aA Tao,pessel’s Ftmula [Flot oy Ate OH, tL ay, +L lly, +aly,) ob Lage) rind 40e vale OF 100) ok a=0-0% tom eu follocg gable ueing | bessel's Fotmmuta. pA % ar ad) et P45 0) 91023 a F 0 “qxoottrs oO: a Ro en 009%F 4,090) 90001 005 Ol ooo as soy | 70-000 poor ontoae onal, < 20-000{ ~9-000] “44 (bos eR otnat | Quo east Ye, 14 foros OY, WNT Sth 4 | Given Mook t9. fend, es a : lestmate. FID, ok te eft ae by using betel er 20026 HH. |o. +g 5 [e oor = [0 Cool +o)+t ¢ o1paet) st 0/0001 +0) « s Laer ya. er] 7 or sg ‘5 Syumula : 3 oes : o28¢ orelbo 0-048, 4 O336 o-0NR be tag OTS, ogy TOATR |) 4 y Jeo . 18 gaygg VISE : ay, ite oh oa : 1-5 6¢0 Oren =yo wl atte wot 20 0 as i seb el ak lensar one id UBMs boye) 840) | = &8¢0 ex ley x Ol, gr g pe Wy * }