‫ حيدر كاظم زغير‬.‫م‬.‫م‬
Secant Method
‫المحاضرة الخامسة‬
Suppose a continuous function
defined on the interval
Secant Method:
[a,b] is given, but now we do not force the iterates to bracket a
root. The graph of the function f is approximated by a secant line,
we get
f (b)  f (a) f (b)  y
f (b)  f (a) f (b)  0
af (b)  bf (a)

 x1 


ba
b  x1
ba
bx
f (b)  f (a)
Secant line
bf ( x1 )  x1 f (b)
Similarly x2 
f ( x1 )  f (b)
In general xi  2 

y=f(x)
xi f ( xi 1 )  xi 1 f ( xi )
; i=0, 1, …
f ( xi 1 )  f ( xi )
(x2,0)
 (a,0)

(b,0)
(x1,0)

xi+2 is an approximate root if |xi+2-xi+1|< for any i.
Ex:
Find the root of the function
by using Secant
method with
Solution :
Let
(
)
(
( ) (
( )
)
)
( )
(
(
)
)
( )
Continue
to
(
(
compute
)(
)
where
)
(
)
.
.
.
|
|
|
|
‫ حيدر كاظم زغير‬.‫م‬.‫م‬
‫المحاضرة الخامسة‬
Secant Method
(
n
)
0
1
-5
1
2
14
2
1.2631578947
-1.6022743840
3
1.3388278388
-0.4303647480
4
1.3666163947
0.0229094308
5
1.3652119026
-0.002990679
6
1.3652300011
-0.0000002032
Note:
In method of false Position on the interval [
(
(
)(
)
(
)(
(
)
)
(
)
)
(
)
while in Secant method
in the same interval .