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67.1 Introduction to mnewton | ||

67.2 Functions and Variables for mnewton |

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`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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__Option variable:__**newtonepsilon**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

__Option variable:__**newtonmaxiter**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

__Function:__**mnewton***(*`FuncList`,`VarList`,`GuessList`)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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