IOSR Joul of Mhemcs IOSR-JM e-issn: 78-578 -ISSN: 39-765X Volume Issue 5 Ve VII Se - Oc6 PP 76-85 wwwosoulsog Jcob Smly sfomo fo SVD d hoov Regulzo fo Les Sues Poblem: he heoecl foudo Sehe Ehdmhe Uwmus Deme of Mhemcl Sceces Kog Se Uvesy Aygb Kog Se Absc: he e eses soluo o Les sues euo s dve by Sgul Vlue Decomoso SVD obed fom usg Jcob Smly sfomo whou ecouse o hoov egulzo mee We use he LU decomoso d QR lgohm s bses of comso fo he obed esuls A olyoml f of ode fve fo he Les sues oblem ws doed Smle umecl d oblem ws obed s my souce od Kog Se Uvesy Aygb showg he fucol elosh bewee emeue d Relve Humdy I s suggesed h he SVD s umeclly bcwd sble s esed o by he LU decomoso mehod elve o sml esuls comued by QR d ohe ow mehods Keywods: les sues euo sgul vlue decomoso Jcob smly sfomo lgohm vese oblems AMS subec Clssfco 65G4 65F5 I Ioduco I he e we cosde les sues euo s lcble o modellg my Scefc oblems usg SVD obed fom Jcob Smly sfomo []Les sues euo belogs o he clss of mos oweful vese oblems whch dels wh he ocess of clculg fom gve se of obsevos he cusl fcos whch oduce hem Such suos wee ledy ofe ecoueed ocs d couscs commuco heoy d lguge ocessg clculo of he desy of he eh mesuemes of s gvy feld medcl mgg comue vso oceoghy soomy emoe sesg mche leg d o-desucve esg [] Bsc ools fo dscussos e vese fuco heoems fo se vlued ms eguly os fo Lschz fuco chcezo of gel d mec eguly d Lschz behvou of mulfuco coeco wh closed cove gh heoem[3 4] he dsce bewee eguly d sog eguly of se vlued m F : X Y whch he Jcob m my be vesged fo oeess oologcl sce foms he bss of ou dscusso hs c be vefed usg heoem due o [5] whch ses h evl m [A] s sogly egul f md A] ] d [ ] [ A whch my be we u o fco whee s he sgul vlue of he m A decesg ode he elve dsce fo whch m A s sgul o he se of sgul A s s gul A mces some om s defed s ds A m A A he ecocl of codo umbe c be eeed s mesue of eess o sguly of he m A d heefoe ds A K A As esul [6] oved h fo such sgul m A A hee holds he esme: A h s fo b A A A K A b A A b A K A we hve Ioduced hus o he dscusso s he well ow Holde s om defed he fom DOI: 979578-577685 wwwosoulsog 76 Pge
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Jcob Smly sfomo fo SVD d hoov Regulzo fo Les Sues Poblem: IV Numecl Eemes Emle he eemel d wee g s my souce fom RODAN Aygb Kog Se Uvesy s showed ble SN DAEIME -4-4 3-4 -8-8 -8 - - - - - 3- - - 3- -7-7 -7-6 -6-3 -3 3-3 -5-5 - - - - - - -9-9 -9 ble EMPERAURE X 396 333634 9887573 76463 643887 6986 33966 8355457 863878 367793 3435 363575 96744 886789 9588 648773 7984 69459 8987 787376 3395 334677 333333 363983 936996 947345 8766 889984 8458 7455 74785 75395 6664 659674 O RELAIVE HUMIDIY % Y 6796866 684359 749686 87566 83368 8345398 475699 373 59693 666683 6444 55738473 39557 4495453 4797735 835739 7994463 844995 789 7953775 636848 5478859 653497 73495656 753975 7653 66996 7698347 87376 86998 894369 83485 899554 835695 I s suggesed h emeue s deede vble X d h Relve Humdy s he deede vble Y We use wdows 7 veso of MALAB fo he clculos d se of esuls flog o hmec s dslyed ble ble showg Resuls comued fo he cosdeed mehods decomoso QR decomoso Sgul vlue hoov decomoso mehod LU mehod fo 3 ^ e+6* 467 449 64 5 mehod fo 3 ^ e+9* 34 6977 9778 3 ^ e+6* 49 38 59 5 Regulzo mehod 34 wh [] ^ 3 6 3 6 e * DOI: 979578-577685 wwwosoulsog 8 Pge
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Jcob Smly sfomo fo SVD d hoov Regulzo fo Les Sues Poblem: VI Cocluso he e suded use of sgul vlue decomoso obed fom Jcob smly sfomo fo he soluo of les sues oblem We comed oes wh sml esuls comued by he LU Fcozo d QR lgohm Smle umecl emle ws e s my souce d fom RODAN Cee fo Lowe Amoshec Sudes Kog Se Uvesy Aygb Kog Se Nge fo he emeue d Relve Humdy fo eod of hy fou mohs whch ws he me ge he Cee fo Lowe moshec Sudes ws esblshed A olyoml f of ode fve ws used Numecl esuls comued by he bove med mehods e gve ble We lso llused he esuls comued fo he uose of foecsg s show Fgues -3 I s suggesed h hee s sog coelo he d s see fom Fgue 3 s esul of coley bewee LU decomoso d SVD A effce evl bsed mehod fo smuleously efg zeos of olyoml whe coeffces e eessed he fom of ucey ws dscussed he sese Peovc [ 6] fo he uose of esy ccessbly o he edes I comug wh Jcob mehod oe fs sfoms o symmec m o symmec m I s ecommeded h whe m A s ely dgol Jcob smly sfomo mehod wll lwys hve ue hd ove QR mehod ovded h oe sog ceo s secfed fo Jcob s mehod [6] Refeeces [] Wlso JH 965: he Algebc Egevlue Poblem Cldo Pess Ofod [] Wled : Ivese Poblem he fee ecycloed ; Auhoy Cool:NDL:57748 Jue 5 [3] Uwmus SE 5 Gh Comleo cluso sooe fo Ievl Les Sues Euo Amec Joul of Mhemcs d Sscs 5 4-3 [4] Neume A 99: Ievl mehods fo sysems of euos Cmbdge Uvesy Pess Cmbdge [5] Rum SM 996: he dsce bewee eguly d sog eguly I G Alefeld d B Lg edos Scefc Comug d Vlded Numecs Vol 9 of Mhemcl Resech P 5-7 [6] Boc A 9: Numecl Mehods Scefc Comug Vol SIAM Phldelh [7] L W 8: Lecue Noes of M Comuos Deme of Mhemcs Nol sg Hu Uvesy Hschu w 343ROC [8] Oeg JM Rhebold WC : Ieve Soluo of Nole euos sevel vbles Clsscs Aled Mhemcs SIAM Phldelh USA [9] Neume A: Ioduco o Numecl lyss Cmbdge Uvesy PessCmbdge [] Roh J 5: A Hd boo of esuls o evl le oblems Czech Acdemy of Sceces Pgue Czech Reublc Euoe Uo;5wwwcscsczoh [] Peovc MRcc L d Mlosevc D 6:Lgueel-Le mehods fo he smuleous omo of olyoml mulle zeos; Yugoslv Joul of Oeos Resech 6 3-44 [] Soe J d Bulsch R 98: Ioduco o Numecl Alyss Sge Velg New Yo [3] Uwmus SE d Ou FO : Comuo of Egevlues of Hem M v Gves Ple Roos Nge Joul of Aled Scece Vol P -6 [4] Golub G d V-Lo F983:M Comuoshe Johs Hos Uvesy PessBlmoe Myld [5] Sef W 8: ol vo egulzo fo le ll-osed vese oblems: Eesos d lco PhD hess Gdue College Azo Se Uvesy USA [6] Uwmus SE4:Regulzo of No-smooh fuco whose Jcob s ely sgul o sgul Amec Ieol Joul of Coemoy Scefc Resech-8 ISSN 349-445 [7] Mye G 998: Eslo-flo wh cocve evl fucos Alcos of Mhemcs 434 4-54 [8] Peovc MS 989: Ieve mehod fo smuleous cluso of olyoml zeos 387 Sge Velg [9] Peovc MS d covc S 995: Zeo fdg mehods of Fouh Ode Joul of Comuol d Aled Mhemcs No 64 P 9-94 [] Fme MR d Lozu G 977: A Algohm fo he ol o Pl Fcozo of olyoml Mhs Poc Cmb PhlSoc No 8 P 47-437 DOI: 979578-577685 wwwosoulsog 85 Pge