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27 lines
645 B
Lua
27 lines
645 B
Lua
-- bisection method for solving non-linear equations
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delta=1e-6 -- tolerance
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function bisect(f,a,b,fa,fb)
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local c=(a+b)/2
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io.write(n," c=",c," a=",a," b=",b,"\n")
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if c==a or c==b or math.abs(a-b)<delta then return c,b-a end
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n=n+1
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local fc=f(c)
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if fa*fc<0 then return bisect(f,a,c,fa,fc) else return bisect(f,c,b,fc,fb) end
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end
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-- find root of f in the inverval [a,b]. needs f(a)*f(b)<0
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function solve(f,a,b)
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n=0
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local z,e=bisect(f,a,b,f(a),f(b))
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io.write(string.format("after %d steps, root is %.17g with error %.1e, f=%.1e\n",n,z,e,f(z)))
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end
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-- our function
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function f(x)
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return x*x*x-x-1
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end
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-- find zero in [1,2]
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solve(f,1,2)
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