## how solve nonlinear equations ?

ahmed ashiry

### ahmed ashiry (view profile)

님이 질문을 제출함. 18 Feb 2015
최근 활동 Erik S.

### Erik S. (view profile)

님이 답변함. 18 Feb 2015
Erik S.

### Erik S. (view profile)

님이 답변을 채택함.
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???????????????????/

표시 이전 댓글 수: 2
ahmed ashiry

18 Feb 2015
yas i has
Erik S.

### Erik S. (view profile)

18 Feb 2015
Since it is an overdetermined system (more equations than variables) is it a least squars solution you need or what do you mean by solution?
ahmed ashiry

### ahmed ashiry (view profile)

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

로그인 to comment.

## 답변 수: 1

Erik S.

### Erik S. (view profile)

님의 답변 18 Feb 2015
채택된 답변

Look in the documentation for the function lsqnonlin
It can solve nonlinear least squares problems.

로그인 to comment.

Translated by