INTERPOLATION(2) ELM1222 Numerical Analysis. ELM1222 Numerical Analysis Dr Muharrem Mercimek
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1 ELM Numerl Alss Dr Murrem Merme INTEROLATION ELM Numerl Alss Some of te otets re dopted from Luree V. Fusett Appled Numerl Alss usg MATLAB. rete Hll I. 999
2 ELM Numerl Alss Dr Murrem Merme Tod s leture eewse ler terpolto eewse qudrt terpolto Cu sple terpolto
3 Sple Iterpolto eewse Ler Iterpolto Smplest form of peewse poloml terpolto Iterpolte te dt wt peewse ler futo wt pots: dt of Set ] [ ] [ ] [ sutervls tree Defe I I I ELM Numerl Alss Dr Murrem Merme
4 ELM Numerl Alss Dr Murrem Merme eewse Ler Iterpolto Emple : eewse Ler Iterpolto Usg [ ] [ ] Futo s otuous ut ot smoot
5 eewse Qudrt Iterpolto Nodes: Were te tervls meet to e te mdpots etwee te dt pots were te futo vlues re gve roessg: dt pots Defe ode pots Spg etwee oseutve dt pots Reltosps: wt futos tervls gve pots ELM Numerl Alss Dr Murrem Merme
6 eewse Qudrt Iterpolto We defe Se Equtos t te teror odes mpose otut odto o te polomls ; ]: [ o ; ]: [ o ; ]: [ o ; ]: [ o ; : ; : ; : for terefore futos tervls gve pots ELM Numerl Alss Dr Murrem Merme
7 eewse Qudrt Iterpolto Equtos t te teror odes [mpose otut odto o te frst dervtve of te polomls] We ve equtos & 8 uow oeffets ; : ; : ; : d gves gves Settg d determe We Se. Equtos for te oeffets t te ero slope odtos t te ed pots of te tervl 7 ELM Numerl Alss Dr Murrem Merme
8 ELM Numerl Alss Dr Murrem Merme 8 eewse Qudrt Iterpolto Emple Dt A pots:.79.7 eewse terpoltg poloml o [..] o [..] o [..] o [..] r. Soluto :oeffe ts : Usg Guss ellmto [ ]
9 eewse Cu Iterpolto Cu sples peewse u poloml Clulto of te oeffets of u poloml Cu sple futo S Spg etwee vlues su tervls gve pots toorder. up wt otuous dervtve u A peewse teform : Splefuto of S 9 ELM Numerl Alss Dr Murrem Merme
10 eewse Cu Iterpolto te u futo s From defto of Determe te vlue of d. we wrte... For d ELM Numerl Alss Dr Murrem Merme
11 ELM Numerl Alss Dr Murrem Merme eewse Cu Iterpolto Costruto of u sple... : equtos for uows... Nturl u sple ssgs d dervtve s ero t te edpots d
12 Nturl Cu Sple Iterpolto Emple ; : ; : ; : s follows : Te equto for u sple. turl for d for e tervls 8. d pots : Cosder dt d Susttutg te vlues for gves for Solvg gves for Solvg ELM Numerl Alss Dr Murrem Merme
13 ELM Numerl Alss Dr Murrem Merme Nturl Cu Sple Iterpolto Te u sple smplfes to : S
14 ELM Numerl Alss Dr Murrem Merme Ruge Futo f [....]; [ ]; Emple for... Here S As osdered turl u sple = 8.87 = -.8 = 8.87 Solvg for & gves =.77 = -. =. = -. = -. =. = -. =.77
15 ELM Numerl Alss Dr Murrem Merme Cu Sple Iterpolto Ceml reto of dt Emple [ ] [ ] Coluso: Curve s smooter t ger degree poloml [ Fg. 8.] Addtol dt pots do ot rell mprove te ppere of orgl urve [Fg. 8.]
16 ELM Numerl Alss Dr Murrem Merme Cu Sple Iterpolto Emple : Dffult dt Dt pots: [.... ] [ ]... 7 Here 8. Solvg for & gves = =. = -. =. =.89 =. 7 = -. 8 =. As osdered turl u sple = -.88 = 7. = -.7 =.8 = -.7 = 7. 7= = =. = -. =. =.89 =. =-. 7 =. 8 =
17 Resultg peewse futo mde te followg poloml Cu Sple Iterpolto 7 ELM Numerl Alss Dr Murrem Merme
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