comparison: tests/fail/demo_bisect.lua
tests/fail/demo_bisect.lua
- changeset 57
- 3e148db7f933
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| 56:d02c7932cbf2 | 57:3e148db7f933 |
|---|---|
| 1 -- bisect.lua | |
| 2 -- bisection method for solving non-linear equations | |
| 3 | |
| 4 delta=1e-6 -- tolerance | |
| 5 | |
| 6 function bisect(f,a,b,fa,fb) | |
| 7 local c=(a+b)/2 | |
| 8 io.write(n," c=",c," a=",a," b=",b,"\n") | |
| 9 if c==a or c==b or math.abs(a-b)<delta then return c,b-a end | |
| 10 n=n+1 | |
| 11 local fc=f(c) | |
| 12 if fa*fc<0 then return bisect(f,a,c,fa,fc) else return bisect(f,c,b,fc,fb) end | |
| 13 end | |
| 14 | |
| 15 -- find root of f in the inverval [a,b]. needs f(a)*f(b)<0 | |
| 16 function solve(f,a,b) | |
| 17 n=0 | |
| 18 local z,e=bisect(f,a,b,f(a),f(b)) | |
| 19 io.write(string.format("after %d steps, root is %.17g with error %.1e, f=%.1e\n",n,z,e,f(z))) | |
| 20 end | |
| 21 | |
| 22 -- our function | |
| 23 function f(x) | |
| 24 return x*x*x-x-1 | |
| 25 end | |
| 26 | |
| 27 -- find zero in [1,2] | |
| 28 solve(f,1,2) | |
| 29 |
