# how solve nonlinear equations ?

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ahmed ashiry on 18 Feb 2015
Answered: Erik S. on 18 Feb 2015
how to solve nonlinear equations ?
these 9 equations in 3 unknown but nonlinear
31.65951=sqrt((20460991.052399-x)^2+(11012393.207537-y)^2+(13140061.841029-z)^2)-sqrt((20462649.31-x)^2+(11012196.356-y)^2+(13137623.266-z)^2) 243.75898=sqrt((1704791.07688-x)^2+(20550181.098118-y)^2+(16863812.406607-z)^2)-sqrt((1706135.95-x)^2+(20548561.881-y)^2+(16865760.323-z)^2) -349.85327=sqrt((18327975.818007-x)^2+(1722639.77547-y)^2+(18786981.252914-z)^2)-sqrt((18326680.829-x)^2+(1720514.194-y)^2+(18788376.839-z)^2) -575.16382=sqrt((12050174.649623-x)^2+(-9980816.456693-y)^2+(21382458.132242-z)^2)-sqrt((12049062.298-x)^2+(-9983309.044-y)^2+(21381885.534-z)^2) 441.83588=sqrt((6415962.553149-x)^2+(15826350.755284-y)^2+(20754833.300093-z)^2)-sqrt((6418526.123-x)^2+(15826408.315-y)^2+(20754019.037-z)^2) -255.03605=sqrt((18966834.575125-x)^2+(6395897.26812-y)^2+(17720969.794907-z)^2)-sqrt((18965851.475-x)^2+(6393896.947-y)^2+(17722730.048-z)^2) 258.29132=sqrt((26283508.487939-x)^2+(-1051136.220342-y)^2+(4730820.234619-z)^2)-sqrt((26282933.567-x)^2+(-1051377.055-y)^2+(4733941.445-z)^2) -550.04848=sqrt((15456741.418182-x)^2+(19573966.047127-y)^2+(-9158923.170409-z)^2)-sqrt((15456435.97-x)^2+(19572808.522-y)^2+(-9161842.101-z)^2) 549.43288=sqrt((25702282.7043-x)^2+(2962424.062583-y)^2+(-6373870.064627-z)^2)-sqrt((25703029.058-x)^2+(2962107.626-y)^2+(-6370839.228-z)^2) but when using solve function [x,y,z] = solve('sqrt((20460991.052399-x)^2+(11012393.207537-y)^2+(13140061.841029-z)^2)-sqrt((20462649.31-x)^2+(11012196.356-y)^2+(13137623.266-z)^2)=31.65951', 'sqrt((1704791.07688-x)^2+(20550181.098118-y)^2+(16863812.406607-z)^2)-sqrt((1706135.95-x)^2+(20548561.881-y)^2+(16865760.323-z)^2)=243.75898', 'sqrt((18327975.818007-x)^2+(1722639.77547-y)^2+(18786981.252914-z)^2)-sqrt((18326680.829-x)^2+(1720514.194-y)^2+(18788376.839-z)^2)=-349.85327', 'sqrt((12050174.649623-x)^2+(-9980816.456693-y)^2+(21382458.132242-z)^2)-sqrt((12049062.298-x)^2+(-9983309.044-y)^2+(21381885.534-z)^2)=-575.16382', 'sqrt((6415962.553149-x)^2+(15826350.755284-y)^2+(20754833.300093-z)^2)-sqrt((6418526.123-x)^2+(15826408.315-y)^2+(20754019.037-z)^2)=441.83588', 'sqrt((18966834.575125-x)^2+(6395897.26812-y)^2+(17720969.794907-z)^2)-sqrt((18965851.475-x)^2+(6393896.947-y)^2+(17722730.048-z)^2)=-255.03605', 'sqrt((26283508.487939-x)^2+(-1051136.220342-y)^2+(4730820.234619-z)^2)-sqrt((26282933.567-x)^2+(-1051377.055-y)^2+(4733941.445-z)^2)=258.29132', 'sqrt((15456741.418182-x)^2+(19573966.047127-y)^2+(-9158923.170409-z)^2)-sqrt((15456435.97-x)^2+(19572808.522-y)^2+(-9161842.101-z)^2)=-550.04848', 'sqrt((25702282.7043-x)^2+(2962424.062583-y)^2+(-6373870.064627-z)^2)-sqrt((25703029.058-x)^2+(2962107.626-y)^2+(-6370839.228-z)^2)=549.43288')
the solution was empty x = [ empty sym ] y = [] z = []
why???????????????????/
ahmed ashiry on 18 Feb 2015
i tried to solve it manually by linearized these equation using Taylor's series and then solve using least square X= inv(A'A) A' L but the results was wrong i see the probelm in manual solution is the linearization step and the large estimation process so i want to find x y z using software

Erik S. on 18 Feb 2015
Look in the documentation for the function lsqnonlin
It can solve nonlinear least squares problems.