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From: <HIDDEN>
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Subject: Re: solving matrices of non liner third order type
Date: Wed, 15 May 2013 09:55:09 +0000 (UTC)
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"Hari Kishore  " <harikishoreguptha@gmail.com> wrote in message <kmvibo$3rj$1@newscl01ah.mathworks.com>...
> "Torsten" wrote in message <kmve6l$mq3$1@newscl01ah.mathworks.com>...
> > "Hari Kishore  " <harikishoreguptha@gmail.com> wrote in message <kmvcrf$jbj$1@newscl01ah.mathworks.com>...
> > > hiii.. 
> > > i tried to solve this matrices but i couldnot because it ends up with non linear third order equations please help me out in this issue and give a program to solve this....
> > > your help is highly appriciated!!
> > > syms bcf0 bcf1 bcf2 bcf3 bcf4 bcf5 q0 q1 q2
> > > 
> > > 
> > > amatrix=[ 12.0,            0, 9.0, 12.0,       0,  9.0; 12.0, 4.39*10^(-4), 9.0, 12.0,       0,  9.0; 12.0,            0, 9.0, 12.0,       0,  9.0; 12.0,            0, 9.0, 12.3,       0, 9.01; 12.0,            0, 9.0, 12.0, 0.00703,  9.0; 12.0,            0, 9.0, 12.0,       0,  9.0];
> > > 
> > > 
> > >  acoeff=[ bcf0;bcf1;bcf2;bcf3;bcf4;bcf5];
> > >  
> > >  
> > >  bmatrix =[           47.3,          42.3,           19.4; -1.63*10^(-19), 4.53*10^(-21), -1.03*10^(-15);1.69,          3.52,           1.47;23.6,          21.1,            9.7;-2.45*10^(-19), 6.79*10^(-21), -5.17*10^(-16);0.844,          1.76,          0.737];
> > >  
> > >  bcoeff=[q0^2;q1^2;q2^2];
> > >  
> > > cmatrix =[    16.4,  -0.0774,    0.193; -0.0774,    0.724, -0.00177;  0.193, -0.00177,   0.0645];
> > > 
> > > ccoeff=[q0;q1;q2];
> > > dmatrix =[          1.65,         0.0571,       0.00251,         -1.65,        -0.127,      -0.00528;2.45*10^(-18), -4.26*10^(-19), 7.37*10^(-20), 7.09*10^(-17), 4.26*10^(-19), 4.58*10^(-19);0.00302,   8.52*10^(-4),  6.98*10^(-5),       -0.0733, -9.76*10^(-4), -6.98*10^(-5)];
> > > 
> > > dcoeff=[bcf0*q0;bcf1*q1;bcf2*q2; bcf3*q0;bcf4*q1;bcf0*q2];
> > > 
> > > (amatrix)*(acoeff)=bmatrix*(bcoeff);
> > > %from first statement find bcf values and use it in second equation
> > > (cmatrix)*(ccoeff)=dmatrix*(dcoeff);
> > > %from second equation find the q0 q1 q2 value
> > 
> > I don't see an easier way than using MATLAB's FSOLVE for your system of nonlinear equations.
> > 
> > Best wishes
> > Torsten.
> Hi. mr.torsten..
> please can you give the code for that operation?

x0 = [-5; -5; -5; -5; -5; -5; -5; -5; -5];  % Make a starting guess at the solution
options = optimoptions('fsolve','Display','iter'); % Option to display output
[x,fval] = fsolve(@myfun,x0,options) % Call solver

function F = myfun(x)
bcf0=x(1);
bcf1=x(2);
bcf2=x(3);
bcf3=x(4);
bcf4=x(5);
bcf5=x(6);
q0=x(7);
q1=x(8);
q2=x(9);

amatrix=[ 12.0,            0, 9.0, 12.0,       0,  9.0; 12.0, 4.39*10^(-4), 9.0, 12.0,       0,  9.0; 12.0,            0, 9.0, 12.0,       0,  9.0; 12.0,            0, 9.0, 12.3,       0, 9.01; 12.0,            0, 9.0, 12.0, 0.00703,  9.0; 12.0,            0, 9.0, 12.0,       0,  9.0]; 
 acoeff=[ bcf0;bcf1;bcf2;bcf3;bcf4;bcf5]; 
 bmatrix =[           47.3,          42.3,           19.4; -1.63*10^(-19), 4.53*10^(-21), -1.03*10^(-15);1.69,          3.52,           1.47;23.6,          21.1,            9.7;-2.45*10^(-19), 6.79*10^(-21), -5.17*10^(-16);0.844,          1.76,          0.737]; 
 bcoeff=[q0^2;q1^2;q2^2]; 
cmatrix =[    16.4,  -0.0774,    0.193; -0.0774,    0.724, -0.00177;  0.193, -0.00177,   0.0645]; 
ccoeff=[q0;q1;q2]; 
dmatrix =[          1.65,         0.0571,       0.00251,         -1.65,        -0.127,      -0.00528;2.45*10^(-18), -4.26*10^(-19), 7.37*10^(-20), 7.09*10^(-17), 4.26*10^(-19), 4.58*10^(-19);0.00302,   8.52*10^(-4),  6.98*10^(-5),       -0.0733, -9.76*10^(-4), -6.98*10^(-5)]; 
dcoeff=[bcf0*q0;bcf1*q1;bcf2*q2; bcf3*q0;bcf4*q1;bcf0*q2]; 

F=[amatrix*acoeff-bmatrix*bcoeff; cmatrix*ccoeff-dmatrix*dcoeff]; 

By the way: bcf0=bcf1=bcf2=bcf3=bcf4=bcf5=q0=q1=q2=0 is a solution which
might complicate the solution process.
Furthermore, scaling of your equations might be necessary because of the 
difference in magnitude of the matrix coefficients.

Best wishes
Torsten.