An Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc. Matrix eigenvalues of jacobi iterative method for solving

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1 [Type tet] [Type tet] [Type tet] ISSN : Volume Issue BoTechology 4 Id Jourl FU PPER BTIJ 4 [77-75] tr egevlues of co tertve method for solvg Yuhu Cu Jgguo Qu Qggog College Hee Uted Uversty Tgsh CHIN E-ml : qugguo@6.com BSTRCT Nowdys the developmet formto techology s rpd. themtcs s ppled more wdely reserch. Egevlue s lso successfully ppled my felds. Ths pper descres the defto of egevlues d gves cocrete emples the frst plce. Net t llustrtes the theoretcl owledge of Jco terto method. From the perspectve of represetto methods t dscusses the represetto method of ler equtos d mtr represetto method. ewhle the Jco terto mtr s proposedd t tells the tertve process Jcques rto. g uder codtos of ctul techg stuto d the use of fuzzy comprehesve evluto methodthe model evlutes the represetto of ler equtos d mtr represetto method for prctcl techg method pplclty. Clculted y the softwre progrmmg the oted results shows tht from comprehesve pot of vew to cosder techg crred out presetto method of ler equtos tertve method s the most pproprte. Flly specfc emples of Jco terto method s gve. KEYWORS tr egevlue; Jco terto method represetto of ler equtos; tr represetto; Fuzzy comprehesve evluto. Trde Scece Ic.

2 78 tr egevlues of co tertve method for solvg BTIJ 4 INTROUCTION Egevlues of mtr plys mportt roles my res such s mge processg. Bsed o the egevlues of the mtr t c e used s the processg of the mge. I the mechcl system the egevlues of the mtr c e used s the ss to determe the equlrum pot. I Wesh o the "Show-shped oudry estmte ts egevlues" emphszed tht the egevlues of the mtr hs my mportt pplctos qutum mechcs d mge processg. The uthor focuses o the questo of the dstruto of egevlues d the estmto prolem. It s dstruto re shows ovl. The pper studys o the dstruto of the egevlues mtr d cocetrte o the dstruto estmtg the rge of egevlues. For the equltes of egevlues squre modulus The model developes udgmet sed o the stlty d the stlty of ler d oler dymcl systems. The cocept lso shows the stlty of tervl mtrces. I 6 Xoq Wu "Jco mtr verse egevlue prolems d other verse prolems" llustrtes the verse prolem of clssfcto d pplcto. escres the three-dgol mtr Jco mtrces orthogol polyomls Guss tegrl d Jco mtr egevlues re the ss o the Jco mtr solvg. The uthors proposes three egevlues Jco lgorthm. They c vod re-costruct the frst Jco mtr of order prcpl sumtr drwcs. These three lgorthms re sed o Newto terpolto d dchotomyguss qudrture formulorthogol mtr decomposto style uts feture vector to Jco mtr form the ss. plce equto for the verse prolem s y solvg the plce equto to solve. Usg severl pecewse ler fucto solutos of ler comtos ppromtes oudry fucto. If the oudry s close to the oudry ler fucto you c fd smlrtes wth the ect soluto of the ppromte soluto. I 6u u "eurl etwor seeg symmetrc mtr egevlues"studys computg egevlues of symmetrc mtr prolems the theoretcl ss of eurl etwors d gves B- orm uchged RNNs model. ccordg to the clculto of the mmum d mmum egevlues he desged the etre progrm to clculte the egevlues d solved the results of umercl epermets. ccordg to the theory of stochstc ppromto methodhe solves the mmum prcpl compoet d lgorthms mmum prcpl elemets. O the ssue of clcultg the geerlzed symmetrc postve defte egevlueshe proposed model of geerlzed egevlue RNNs. The pper descres the cocept of mtr egevlues d geerl solvg methods d dscusses the formulto tertve method d gves resole emple. TRIX EIGENVUE If for order mtr t ests vlue of m the o-zero-dmesol colum vector elg the estlshmet of m d the t s sd tht m s the egevlues to. Colum vector s of the feture vector. The method for solvg egevlues s so my such s the use of me m s the chrcterstc vlue of. If the order mtr ests mtr polyoml equtos g m. the the egevlues of the mtr must comply. I ddto there s Jcotertve methods QR lgorthms d G -S tertve method. Specfc emples: Solvg mtr egevlues. Compges chrcterstc equto E

3 BTIJ 4 Yuhu Cu d Jgguo Qu 79 E Therefore egevlues s JCOBI ITERTIVE ETHO Itertve method represetto cludes ler equtos represetto d mtr equto represetto. I solvg prctcl prolems the covetol egevlue soluto s ot very prctcl. Itertve method for solvg s most resole the clculted results s reltvely ccurte. er equtos represetto ssumg the estece of the order equtos If the mtr s o-sgulr mtr of coeffcets d d the the equto c e rewrtte s Be rewrtte s tertve formt Smplfed s

4 7 tr egevlues of co tertve method for solvg BTIJ 4 4 Whe gve tl vlue T X fter repeted tertve process to derve set of vectors T X f X coverges to T X * * * * the * s the soluto of equtos ths soluto method s clled Jco terto. tr represetto tr equto whch X Costruct sttory terto order: f I N N B f B mogthem Thetlvector 5 ssumg Select the dgol splt to N you c get the tertve method s follows: f J U I B f B mogthem : thetlvector 6 Jco terto mtr If there re three mtrces U stsfy the followg codtos 7

5 BTIJ 4 Yuhu Cu d Jgguo Qu 7 8 U 4 9 Well U tht s dvded to lower trgulr mtr dgol d upper trgulr mtr d thus llustrte the Jco terto mtr of the form J U Jco terto process Jco tertve process cludes plurlty of process eterg the tl codtos. d the results c e oted. Judge error of etwee the clculted d the ect vlue. If the error s too lrge they wt to cotue the tertve process. whe the error s the llowle rge you c determe resole clculto results show Fgure. Fgure : Jco terto process

6 7 tr egevlues of co tertve method for solvg BTIJ 4 FUZZY COPREHENSIVE EVUTION ETHO I geerl the mout of fuzzy comprehesve evluto volves three. The estece of U u u clled fctors set. fctors relted to the oect eg evluted to set up deoted y { u } They set up m ll the possle estece of commet deoted y V { v v } v m clled udge set. Becuse ech fctor's sttus s ot the sme d ts role s ot the sme so there re metrcs tht weght. deoted y { } Comprehesve Evluto Fuzzy comprehesve evluto coducted s follows U u u set of fctors set { u } Settg evluto set V { v v v m } Sgle fctor udge ws r { v v v } 4 Costruct comprehesve evluto mtr: r r r m r r r m R r r rm m computg B o R d eed to e evluted ccordce wth the prcple of mmum degree of memershp. 5 Evluto: For weghts { } efto Opertors Whe comprehesve evluto ccordg to the opertoro to defe dfferet models dfferet there. m fctor determg the type odel Ⅰ: { r } m m The model evluto decde o the fctors plyg mor role the overll evluto. other fctors wll ot ffect the udgmet. Reltvely speg ths model s sutle for comprehesve evluto of the optml sgle udgmet optml stuto. the m fctor promet type model Ⅱ: { r } m m The model d Ⅰ model s smlr ut t s more refed th Ⅰ model. Not oly does t hghlght the m fctors ut lso te to ccout other fctors. Ths model s pplcle to the rge of model Ⅰ ot pplcle vrety of fctors tht s ot ope to dfferet crcumstces ut whe the eed for refemet. Weghted verge type model Ⅲ: m r 4

7 BTIJ 4 Yuhu Cu d Jgguo Qu 7 Ths model s ccordce wth the mportce of the vrous fctors fluecg fctors for ll full cosderto. Reltvely speg t pplyes stuto tht requre comprehesve optml. te smll upper oud d type 4 odel Ⅳ: r m m 5 The model use specl tteto s: Ech c ot get too lrge otherwse ll of the crcumstces my occur; ech c ot get too smll there would e equl to the sum of ech cse whch wll led to sgle evluto fctors relevt formto s lost. Blced verge Type 5 odelⅤ: r r m 6 r r The model s sutle for the stuto tht comprehesve evluto mtr elemet s too lrge or too smll. odel estlshed ths pper usg the m fctor determg the type of opertor. Resole wy of epresso For represetto method tertve method oe represetto method of ler equtos the secod s represetto of mtr equtos method. I the techg process ectly wht method s more sutle for studets to uderstd. Ths ssue for the epso wor of techers s essetl. From the studet's uderstdg of the pplcto of the coveece d ese of techers the techg of these three cosdertos. The pper does comprehesve evluto for these two. fter do lot of vestgto for the relevt techers d studets we c fd fshg s show TBE. TBE : Survey results Equtos tr Studets' uderstdg degree.4.6 Ese of pplcto.8. ffculty of techers tught..7 ccordg to the ctul stutofor ese of studet's uderstdg degreepplcto coveece d techers the techg of these three weghts were ssged..6.. Through softwre progrmmg the results c e clculted B..4. It c e see from comprehesve perspectve of the wor crred out to cosder techg d presetto method of ler equtos tertve method s the most pproprte. EXPES Emple : The rto usg the Jcques tertve method s clculted 5

8 74 tr egevlues of co tertve method for solvg BTIJ 4 Soluto : Usg the represetto method for solvg ler equtos s follows The tl vlue T gve to the results show TBE. TBE : Iterto Results Tle Itertos Soluto : 9 U U J

9 BTIJ 4 Yuhu Cu d Jgguo Qu 75 CONCUSION Egevlues of mtr s mportt scece d egeerg theory. Egevlues covetol methods re ot sutle for solvg prctcl prolems resultg Jco terto method. QR terto method s sutle for the clculto methods to solve prctcl prolems. However the ctul techg process tertve method s ot coducve to studet uderstdg d lerg. I ths pper fuzzy mthemtcs come to ler lger. By fuzzy comprehesve evluto method from the studet's uderstdg degree pplcto of the coveece d ese of techers the techg of these three cosdertos whch cludes Jco tertve method of mtr represetto method. er equtos represetto method s sutle for techg wor commeced represetto method for techg relted wor. It provdes theoretcl ss. CKNOWEGEENTS Ths reserch s supported y the Ntol Nture Foudto of Ch Grt No. 677 d the Ntol Scece Foudto for Hee Provce Grt No.94 ll support s grtefully cowledged. REFERENCES [] Hogme B; Comprtve lyss of Jco d Guss-Sedel Itertve ethod Covergece of Itertve ethods [J] Hulueer College [] Heg u Kulg Xu; Jco d Guss-Sedel Iterto ethod for Solvg er Equtos lyss d pplcto[j] Qug Techers College [] Chghe u; Compre Jco Itertve ethod d Proecto ethod of Solvg er Equtos [J] Beg Isttute of rchtecturl Egeerg [4] Xoq Wu; Jco tr Iverse Egevlue Prolems d other Iverse Prolem [] Shgh Uversty Ph thess 6. [5] Wesh o; Estmtes d ther Ehto-Shped Boudry Egevlues[] Chogqg Uversty mster's degree thess. [6] u u; Symmetrc tr Egevlues Neurl Networs [] l Uversty of Techology Ph thess 6. [7] Jwu Zhuo; tl pplctos themtcl odelg [] Beg: Beg Uversty of eroutcs d stroutcs Press. [8] Yogzheg Zhou; themtcl odelg [] Shgh: Tog Uversty Press. [9] Xghuo W; Prolty Theory d themtcl Sttstcs [] Beg: Scece Press 7. [] Xoy Wg; themtcl odelg d themtcl Epermet [] Beg: Scece Press.