March 2014
Intermediate to advanced
412 pages
11h 16m
English
Content preview from Numerical Methods and Optimization
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Chapter 4
Solving Equations
In this chapter, we discuss several numerical methods for solving a nonlinear
equation in the form
F (x)=0, (4.1)
where F (x) is a given real function.
Definition 4.1 Anumberx
∗
such that F (x
∗
)=0is called a root of the
function F (x) or of the equation F (x)=0.
The problem of finding a root of a function (equation) arises frequently in
science, engineering and everyday life.
Example 4.1 John saves money by making regular monthly deposits in the
amount p to his account. Assume that the annual interest rate is r. Then the
total amount, A, that John will have after n payments is
A = p + p
1+
r
12
+ p
1+
r
12
2
+ ...+ p
1+
r
12
n−1
. (4.2)
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