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Octave can solve sets of nonlinear equations of the form
F (x) = 0
using the function fsolve, which is based on the Minpack
subroutine hybrd.
Given fcn, the name of a function of the form
f (x)and an initial starting point x0,fsolvesolves the set of equations such thatf(x) == 0.If fcn is a two-element string array, the first element names the function f described above, and the second element names a function of the form
j (x)to compute the Jacobian matrix with elementsdf_i jac(i,j) = ---- dx_jYou can use the function
fsolve_optionsto set optional parameters forfsolve.
When called with two arguments, this function allows you set options parameters for the function
fsolve. Given one argument,fsolve_optionsreturns the value of the corresponding option. If no arguments are supplied, the names of all the available options and their current values are displayed.Options include
"tolerance"- Nonnegative relative tolerance.
Here is a complete example. To solve the set of equations
-2x^2 + 3xy + 4 sin(y) = 6
3x^2 - 2xy^2 + 3 cos(x) = -4
you first need to write a function to compute the value of the given function. For example:
function y = f (x)
y(1) = -2*x(1)^2 + 3*x(1)*x(2) + 4*sin(x(2)) - 6;
y(2) = 3*x(1)^2 - 2*x(1)*x(2)^2 + 3*cos(x(1)) + 4;
endfunction
Then, call fsolve with a specified initial condition to find the
roots of the system of equations. For example, given the function
f defined above,
[x, info] = fsolve ("f", [1; 2])
results in the solution
x =
0.57983
2.54621
info = 1
A value of info = 1 indicates that the solution has converged.
The function perror may be used to print English messages
corresponding to the numeric error codes. For example,
perror ("fsolve", 1)
-| solution converged to requested tolerance