Subject: tips for Multiple roots of non-algebric equations
From: Luigi Marino
Date: Sat, 3 Jan 2009 10:13:14 +0100
I try to solve non-algebric equations with multiple roots. :
1. first example.
f:log(x^2+1)-sin(x)-4;
for k:-12 thru -3 step 1 do print("x="(newton(f,x,k,0.0000000001)))$
x=(-11.473978752837)
x=(-11.47397875283699)
x=(-10.11683910867541)
x=(-10.11683910866628)
x=(4.448769777051635)
x=(-6.514022226263688)
x=(-6.514022226261542)
x=(-6.514022226263688)
x=(5.817314641920149)
x=(9.004771476502718)
2. second example.
g:log(x+1)-2*x+1;
log(x+1)-2*x+1(%i12)
for k:-0.99 thru 1 step 1 do print("x="(newton(g,x,k,0.0000000001)))$
x=(-0.94435167809671)
x=(0.79153693801855)
3. third example
h:log(x+1)-1/2*x^2+0.6;(%o13)
log(x+1)-x^2/2+0.6(%i14)
for k:0 thru 1 step 1 do print("x="(newton(h,x,k,0.0000000001)))$
x=(-0.40442128319509)
x=(1.806649648414053)
Luigi Marino