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Default value: 10.0^(-fpprec/2)
Precision to determine when the mnewton function has converged towards
the solution. If newtonepsilon is a bigfloat, then mnewton
computations are done with bigfloats. See also mnewton.
Default value: 50
Maximum number of iterations to stop the mnewton function
if it does not converge or if it converges too slowly.
See also mnewton.
Multiple nonlinear functions solution using the Newton method. FuncList is the list of functions to solve, VarList is the list of variable names, and GuessList is the list of initial approximations. The optional argument DF is the Jacobian matrix of the list of functions; if not supplied, it is calculated automatically from FuncList.
The solution is returned in the same format that solve() returns.
If the solution is not found, [] is returned.
This function is controlled by global variables newtonepsilon and
newtonmaxiter.
See also realroots, allroots, find_root and
newton.
(%i1) load("mnewton")$
(%i2) mnewton([x1+3*log(x1)-x2^2, 2*x1^2-x1*x2-5*x1+1],
[x1, x2], [5, 5]);
(%o2) [[x1 = 3.756834008012769, x2 = 2.779849592817897]]
(%i3) mnewton([2*a^a-5],[a],[1]);
(%o3) [[a = 1.70927556786144]]
(%i4) mnewton([2*3^u-v/u-5, u+2^v-4], [u, v], [2, 2]);
(%o4) [[u = 1.066618389595407, v = 1.552564766841786]]
The variable newtonepsilon controls the precision of the
approximations. It also controls if computations are performed with
floats or bigfloats.
(%i1) load("mnewton")$
(%i2) (fpprec : 25, newtonepsilon : bfloat(10^(-fpprec+5)))$
(%i3) mnewton([2*3^u-v/u-5, u+2^v-4], [u, v], [2, 2]);
(%o3) [[u = 1.066618389595406772591173b0,
v = 1.552564766841786450100418b0]]
To use this function write first load("mnewton").
See also newtonepsilon and newtonmaxiter.
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