-
8/13/2019 Mws Com Nle Txt Secant Examples
1/3
Chapter 03.05Secant Method of Solving a Nonlinear Equation More
ExamplesComputer Science
Example 1
To find the inverse of a number , one can use the equationa
0
1
)( cacf
where c is the inverse of .a
Use the secant method of finding roots of equations to find the
inverse of . Conduct
three iterations to estimate the root of the above equation.
Find the absolute relative
approximate error at the end of each iteration and the number of
significant digits at leastcorrect at the end of each
iteration.
5.2a
Solution
01
)( c
acf
1
1
111
)(1
ii
ii
i
ii
ca
ca
ccc
a
cc
ii
ii
i
i
cc
ccc
a
c11
)(1
1
1
1
1
1
)(
)(1
ii
ii
ii
i
i
cc
cc
ccc
a
c
i
iiic
accc1
1
03.05.1
-
8/13/2019 Mws Com Nle Txt Secant Examples
2/3
03.05.2 Chapter 03.05
)1(1 iii accc
Let us take the initial guesses of the root of 0cf as 1.01 c and
.c 6.00
Iteration 1
The estimate of the root is
)1( 0101 acccc
1)6.0(5.2)1.0(6.0 55.0
The absolute relative approximate error a at the end of
Iteration 1 is
1001
01
c
cca
10055.0
6.055.0
%0909.9 The number of significant digits at least correct is 0,
as you need an absolute relative
approximate error of less than for one significant digit to be
correct in your result.%5
Iteration 2
The estimate of the root is
)1( 1012 acccc
1)55.0(5.2)6.0(55.0 325.0
The absolute relative approximate error a at the end of
Iteration 2 is
1002
12
c
cca
100325.0
55.0325.0
%231.69The number of significant digits at least correct is
0.
Iteration 3The estimate of the root is
)1( 2123 acccc 1)325.0(5.2)55.0(325.0
42813.0
The absolute relative approximate error a at the end of
Iteration 3 is
1003
23
c
cca
-
8/13/2019 Mws Com Nle Txt Secant Examples
3/3
Secant Method More Examples: Computer Science 03.05.3
10042813.0
325.042813.0
%088.24 The number of significant digits at least correct is
0.
NONLINEAR EQUATIONS
Topic Secant Method-More Examples
Summary Examples of Secant MethodMajor Computer Engineering
Authors Autar Kaw
Date August 7, 2009
Web Site http://numericalmethods.eng.usf.edu
http://c/Documents%20and%20Settings/sgarapat/http://c/Documents%20and%20Settings/sgarapat/http://c/Documents%20and%20Settings/sgarapat/
