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.TH fsolve G "August 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
fsolve - find a zero of a system of n nonlinear functions
.SH CALLING SEQUENCE
.nf
[x [,v [,info]]]=fsolve(x0,fct [,fjac] [,tol])
.fi
.SH PARAMETERS
.TP 10
x0
: real vector (initial value of function argument).
.TP
fct
: external (i.e function or list or string).
.TP
fjac
: external (i.e function or list or string).
.TP
tol
: real scalar. precision tolerance: termination occurs
when the algorithm estimates that the relative error
between x and the solution is at most tol.
(\fVtol=1.d-10\fR is the default value).
.TP
x :
real vector (final value of function argument, estimated zero).
.TP
v :
real vector (value of function at x).
.TP
info
: termination indicator
.RS
.TP
0
: improper input parameters.
.TP
1
: algorithm estimates that the relative error between x and the solution
is at most tol.
.TP
2
: number of calls to fcn reached
.TP
3
: tol is too small. No further improvement in the approximate solution
x is possible.
.TP
4
: iteration is not making good progress.
.RE
.SH DESCRIPTION
find a zero of a system of
n nonlinear functions in n variables by a modification
of the powell hybrid method. Jacobian may be provided.
.nf
0 = fct(x) w.r.t x.
.fi
\fVfct\fR is an "external".
This external returns \fVv=fct(x)\fR given \fVx\fR.
.LP
The simplest calling sequence for \fVfct\fR is:
.nf
[v]=fct(x).
.fi
If \fVfct\fR is a character string, it refers to a C or Fortran routine
which must be linked to Scilab. Fortran calling sequence must be
.nf
fct(n,x,v,iflag)
integer n,iflag
double precision x(n),v(n)
.fi
and C Calling sequence must be
.nf
fct(int *n, double x[],double v[],int *iflag)
.fi
Incremental link is possible (help \fVlink\fR).
.LP
.fi
\fVjac\fR is an "external".
This external returns \fVv=d(fct)/dx (x)\fR given \fVx\fR.
.LP
The simplest calling sequence for \fVjac\fR is:
.nf
[v]=jac(x).
.fi
If \fVjac\fR is a character string, it refers to a to a C or Fortran routine
which must be linked to Scilab calling sequences are the same as those
for fct. Note however that v must be a nxn array.
.SH EXAMPLES
.nf
// A simple example with fsolve
a=[1,7;2,8];b=[10;11];
deff('[y]=fsol1(x)','y=a*x+b');
deff('[y]=fsolj1(x)','y=a');
[xres]=fsolve([100;100],fsol1);
a*xres+b
[xres]=fsolve([100;100],fsol1,fsolj1);
a*xres+b
// See routines/default/Ex-fsolve.f
[xres]=fsolve([100;100],'fsol1','fsolj1',1.e-7);
a*xres+b
.fi
.SH SEE ALSO
external, quapro, linpro, optim
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