Multidimensional Newton-Raphson method: Difference between revisions

This doesn't use Newton-Raphson (with derivatives) but a hybrid algorithm.

<lang zkl>var [const] GSL=Import.lib("zklGSL"); // libGSL (GNU Scientific Library)

// two functions of two variables: f(x,y)=0

fs:=T(fcn(x,y){ x.atan() - y*y*y }, fcn(x,y){ 4.0*x*x + 9*y*y - 36 });

v=GSL.VectorFromData(2.75, 1.25); // an initial guess at the solution

GSL.multiroot_fsolver(fs,v);

v.format(11,8).println(); // answer overwrites initial guess

xy:=v.toList(); // Vector to List

fs.apply('wrap(f){ f(xy.xplode()) }).println(); // deltas from zero</lang>

2.59807621, 1.06365371

L(2.13651e-09,2.94321e-10)

</pre>

A condensed solver (for a different set of functions):

<lang zkl>v:=GSL.VectorFromData(-10.0, -15.0);

GSL.multiroot_fsolver(T( fcn(x,y){ 1.0 - x }, fcn(x,y){ 10.0*(y - x*x) }),v)

.format().println(); // --> (1,1)</lang>

{{out}}

<pre>

1.00,1.00