# [Maxima] tips for Multiple roots of non-algebric equations

Raymond Toy raymond.toy at ericsson.com
Mon Jan 5 09:51:12 CST 2009

```>>>>> "Luigi" == Luigi Marino <luigi_marino2 at alice.it> writes:

Luigi> I try  to solve  non-algebric equations with multiple roots. :
Luigi> 1. first example.
Luigi> f:log(x^2+1)-sin(x)-4;

Luigi> for k:-12 thru -3 step 1 do print("x="(newton(f,x,k,0.0000000001)))\$

Luigi> x=(-11.473978752837)
Luigi> x=(-11.47397875283699)

Are you bothered that you get the same roots again?

Luigi> 3. third example
Luigi>  h:log(x+1)-1/2*x^2+0.6;(%o13)
Luigi> log(x+1)-x^2/2+0.6(%i14)
Luigi> for k:0 thru 1 step 1 do print("x="(newton(h,x,k,0.0000000001)))\$
Luigi> x=(-0.40442128319509)
Luigi> x=(1.806649648414053)

Are you bothered that you get roots outside of the interval [0,1]?

I think that's the nature of Newton's method.  Your initial guess has
to be close enough to the root to converge to the root; different
starting points can converge to the same root.  And nothing constrains
Newton's method to stay in any given interval.

Ray
```