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Topic: solving matrices of non liner third order type
Replies: 12   Last Post: May 24, 2013 2:30 AM

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Torsten

Posts: 1,454
Registered: 11/8/10
Re: solving matrices of non liner third order type
Posted: May 15, 2013 5:55 AM
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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.



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