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2 False Position

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NUMERICAL METHODS
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  F  ALSE -P OSITION M ETHODOF S OLVINGA  N ONLINEAR E QUATION 19/7/2017  (1) (2) 1 Introduction 2   U   x f   U   x r   x    L  x f    L  x O    x  x Exact root 0)(    x  f   0)(*)(   U  L  x  f   x  f   In the Bisection method 2 U  Lr   x x x   (3) Figure 1 False-Position Method  3 False-Position Method Based on two similar triangles, shown in Figure 1, one gets: U r U  Lr  L  x x x  f   x x x  f    )()( 0;0)( 0;0)(  U r U  Lr  L  x x x  f    x x x  f   The signs for both sides of Eq. (4) is consistent, since: (4)  4          LU r U  Lr   x  f   x x x  f   x x            U  Lr U  L LU   x  f   x  f   x x  f   x x  f   x   From Eq. (4), one obtains The above equation can be solved to obtain the next predicted root        U  LU  L LU  r   x  f   x  f    x  f   x x  f   x  x  r   x , as (5)
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