NewtonRaphsonMethod
NewtonRaphsonMethod
f(x)
[x f( x )]
f(xi)
i,
i
f(xi )
xi +1 = xi
f (xi )
f(xi-1)
xi+2
xi+1
xi
X
Figure1GeometricalillustrationoftheNewtonRaphsonmethod.
2
Derivation
f(x)
f(xi)
tan( ) =
B
AB
AC
f ( xi )
f ' ( xi ) =
xi xi +1
C
A
xi+1
x
Sources of Error
1
Two sources of numerical error
1) Round-off error
2) Truncation error
2
Round off Error
Caused by representing a number
approximately
1
0.333333.
3
2 1.4142.
3
Problems created by round-off error
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