Solve non linear m equations in n unknows with m,n

Hy anyone,

I have to find 3 unknows k(1),k(2),k(3) for 9 non-linear equations. Maybe it's better to define this an optimization problem.

I know three nominal values of the unknowns, and if needed I could try to define a range around these nominal values k0.

F = @(k) [4357202.836588509231357947142360134250944*k(1) + 9859271.851176796611675995847715914277865*k(2) + 12592776.99754481905498970954517604707339*k(3) - 20.51859923348048473398668989105882860955*k(1)*k(2) - 135.0095116969981247839644165367430620599*k(1)*k(3) - 224.418415685580282325042228673779142726*k(2)*k(3) + 0.0001974038864112137491709680455099275622648*k(1)*k(2)*k(3) - 386025229299.9568622662995264786719011713  ;   
          1286149.80914724430143242256559904173928*k(1) + 2910123.182185286538510348586301262416866*k(2) + 2457765.768214964601468842428661712021226*k(3) - 9.979230585365292560599694975564174587835*k(1)*k(2) - 43.09982147759781641104881096543829123567*k(1)*k(3) - 65.27620037797945725044359667927450708008*k(2)*k(3) + 0.00006792607212029985031909708221116361537827*k(1)*k(2)*k(3) - 67420190839.84246007677646398928979376589 ;    
          1291805.705153364176489841145279987563561*k(1) + 2952984.164173089873787405350927883253236*k(2) + 2488522.02733906362837134689575136170105*k(3) - 10.00213358127286743093338940391172830115*k(1)*k(2) - 43.18942706666197475326431587285044438606*k(1)*k(3) - 65.22912805800736162093930913666144406004*k(2)*k(3) + 0.00006800109075884199872551625872697606227797*k(1)*k(2)*k(3) - 67661033001.60213888043923408164910427652 ;    
          12607759.95501730560066220761139765541052*k(1) + 26107099.62399446518954185057851482359657*k(2) + 12260288.70589727224842731242100434358285*k(3) - 22.69101222596863008864367035207016160712*k(1)*k(2) - 95.22704935962102682612616817269934116956*k(1)*k(3) - 189.138544525870320685548774619114313263*k(2)*k(3) + 0.0001354239064903012104673850380188781482234*k(1)*k(2)*k(3) - 1617019494158.855188411491058498370659906  ;    
          3748563.849785500307764636868502067998803*k(1) + 7519193.935007966250602037219051168242994*k(2) + 1920762.425468395419190980660961727263255*k(3) - 10.00195708400526165569539946926743327835*k(1)*k(2) - 25.95996227527224374564055763401515220669*k(1)*k(3) - 46.9993740449578883455888632500556953974*k(2)*k(3) + 0.00004292805192481937357291378153289530770884*k(1)*k(2)*k(3) - 268930294963.1287649791083387067703578281 ;     
          3560167.022800402172529857336016080641268*k(1) + 7095588.500283814732810917180124881872391*k(2) + 1872107.345499261379514804556669792996733*k(3) - 9.746391301799269655619403707441356123279*k(1)*k(2) - 25.98899847891971378456065249962057858545*k(1)*k(3) - 46.71325371351432635875183712080604274365*k(2)*k(3) + 0.00004289814329802416986725607787863446922266*k(1)*k(2)*k(3) - 249358601643.2416914446620002210835035023;      
          3988762.27490288425887479384394653453603*k(1) + 8738461.159895929076620546905704970803657*k(2) + 13368646.02473437900857649140017905564475*k(3) - 18.15434755110089728695928379362075027531*k(1)*k(2) - 119.4530664672458477131331425063832791194*k(1)*k(3) - 186.1280821229015574286430386345502689368*k(2)*k(3) + 0.0001688072891012624325953548233012356174784*k(1)*k(2)*k(3) - 427570770360.0065326896147536792317001875  ;    
          1116806.028299326940326556323008098748303*k(1) + 2410432.013581268638399095955292097454772*k(2) + 2460478.259635752703845834063021936376325*k(3) - 8.508752280537139811312068491475302077003*k(1)*k(2) - 36.74889573411236784198106191846789795424*k(1)*k(3) - 52.75237699668644488968923879393588483896*k(2)*k(3) + 0.0000568706188905800444434832754790718433858*k(1)*k(2)*k(3) - 71210180483.80869174347140705351621299913 ;     
          1112882.251030959336077685981922307508417*k(1) + 2369803.075724879582821621219200347951115*k(2) + 2429550.257798150438894801256125548799455*k(3) - 8.481450605212287042087645383422755941522*k(1)*k(2) - 36.62308540041477474937317212786907166854*k(1)*k(3) - 52.76878192360401510871042697865803726479*k(2)*k(3) + 0.00005675692195390562699333325622768362584587*k(1)*k(2)*k(3) - 70951603858.72984077079782867429825559985];           
k0 = [5.1920e+06,8.2376e+05,4.0222e+05];

Do you have any ideas? Thanks.

Answer 1

[Torsten]

k = lsqnonlin(F,k0)

[Giuseppe Avallone]

This is already a good suggestion. Thank you very much