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• Introduction to mnewton: | ||
• Functions and Variables for mnewton: |
Next: Functions and Variables for mnewton, Previous: mnewton-pkg, Up: mnewton-pkg [Contents][Index]
mnewton
is an implementation of Newton’s method for solving nonlinear
equations in one or more variables.
Categories: Numerical methods Share packages Package mnewton
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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
.
Categories: Package 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
.
Categories: Package 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 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
.
(%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
.
Categories: Package mnewton
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