A simple 2-D interpolation model for analysis of nonlinear data

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1 Vol No - p://oog//n Nl Sn A mpl -D npolon mol o nl o nonln M Zmn Dpmn o Cvl Engnng Fl o nolog n Engnng Yo Unv Yo In; m@ml Rv M ; v Apl ; p M ABSRAC o mnon volm n wg o nonnom o n o po vlon o mnng n o ng o onon mo o npolon ll l v w qnl o npol on-mnonl pln Bpln n Bz v mo v goo n o mnon o gom o nongl m v om lmon n polm w womnonl npolon nl omng lg ln m o qon w lo o n n l non w olon In wo-mnonl pln w v vng o mpl n l omponl opon o pln non ppl v onn o C lmn on pn mol l n o volm o lg n govnng o lo o Kwo: Smlon; Appomon; L q; C Spln; Opmzon; Cv Fng; Pon INRODUCION mo popl mo o npolon o Lgng mo Nvll on ppo Nwon v n mo C pln Hm pln Bpln n Bz mo Fo Nvll n Nwon v n mo g g o polnoml gnon gow In on pln ppo v on o nm o o n gmn v gnl w o v nvl o oll nvl o gmn n on n ppomng polnoml on nvl Appomon non o p ll pw polnoml ppomon mo vng o movng ollo n o g g polnoml In ppo onn o C on gmn on Howv; onn o oponl o wllng omlon o ng pln v l n olon o -gonl m o qon Hm npolon on wo pon p n p n wo ngn vl p n p o pon I omp v gmn p gong n on o p n n p movng ow p Hm npolon n mpon vng Hm v n mo ngng ngn vl Bz v pm v p polnoml non o pm g o polnoml pn on nm o pon o n v mo ppl onol pon n pn n ppomng v Bz v o no p og nnl pon n l pon Innl pon nln on n poon o v pllng ow mlv [-] B-pln mo w popo n o v n B-pln v n ppomng o npolng v vng o B-pln v o Bz v onng g onn o nvl pln gmn [-] I o pl { n} pln non S n on on nvl [ + ] W mol onn o C on on o gmn pln non o g o nvl : g I Eq wn on pon o gmn + n Copg SR

2 M Zmn / Nl Sn - Copg SR vv o pln non ollow on n o nvl n on pll om Eq w lmn z o lmn nvl = + polm w ppo w gnll on v ngn vl n + pon n pov pplng ollowng ppomon qon ow n nl n n w n ppomon pvl o vv pon n o nom nvl ] [ ] [ ] [ ollowng wo mpl ow npolon o wo o ov ppo EXAMPLES Empl mpl n l o gonw ngnng Wn poon wll n nonn q pmp w onnol wwn om og wn q on o pon pog ll ow om wll B o n o g o n om o vl lg n no lzon o w lvl n n q wll onn o ln ppong q nn n l n Howv o ln o onnol on o pon p pl nl qon govnng n- l low n nonl onn q n pol oon m S olon o ov pl nl qon Q ppom ov qon ollowng!! log Q w S = wown n Q = g n gpm = m pmpng n = on o nmv n gllon p p oo gp/ n S = on o og mnonl vl o ql W o npolon v logm vl o W p o [] Fo npolon o o n pon on Fg ow ompon wn W v W mol W Fg ompon wn n mol

3 M Zmn / Nl Sn - Copg SR n mol o nn pln v B on g l n goo lonp wn o Empl In polm o v p o on om pm Eq w non-nom gmn [ ] o n n n n o Ao o pln v gn ong o omlon o Eq n Fg ow lonp wn l vl n npol on A n n lv pl n wn m FORMULAION FOR -D INERPOLAION pln omon ppl o wo mnonl npolon n o no p g o n m noon A g I ov qon wn on o oon o low l pon on gmn Eq Fg ompon wn n mol on n omlon o mnon o on wll mpl o n m noon A ov pln non n pm nnown o gmn o p o; n qon q o nng m Fo qon non vl on n qon ng pl vv n n on o no onn o C on o o o on o v lmn vv n n on o Eq : on n v pll om ng ollowng onon

4 M Zmn / Nl Sn - Copg SR ov n qon gv ln m o qon I olv nlll govnng pm on ollow w PROBLEM Fo ng ov omlon vl polm w on H onl on o m pn o polm on om Eq [] [] z omn o polm on o lmn n no lmn nom w n ov omlon w ppl o o govnng Fg ow npolon v long = = = n = A n n -D mol pn lo lonp o lng o HE RESULS AND CONCLUSIONS In wo mol o -D n -D npolon w pn mol n gow o nl o; n ppl o polm vng g I vng o l omponl o p o pln Bz n B-pln mo pll o -D polm onn o gmn C o; n o mn polm llon o n volm o nonnom o I ommn o omp -D mol w Bz n B-pn mo p o n n ompon mol Fg ompon wn n -D mol

5 M Zmn / Nl Sn - REFERENCES [] Slmon D Cv n o omp gp Spng Nw Yo [] Sn A n S B Comp ngnng gn Spng Anm Pl Nw Dl [] Con SD n Boo C Elmn nml nl n lgom ppo Kn Kong Pnng Co P L Sngpo [] Bn R n F D Nml nl PWS-Kn Plng Compn Boon [] M D Appl gom o omp gp n CAD n Eon Spng-Vlg Nw Yo [] o DK Gonw olog Jon Wl & Son In Nw Yo Copg SR

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