- 1. ROOTS OF EQUATIONS FACULTAD DE INGENIERIAS FISICOQUMICAS
ESCUELA INGENIERIA DE PETRLEOS CYNDY ARGOTE SIERRA INGENIERIA DE
PETRLEOS
2. INTRODUCTION
- The determination of the roots of an equation is one of the
oldest problems in mathematics and there have been many efforts in
this regard. Its importance is that if we can determine the roots
of an equation we can also determine the maximum and minimum
eigenvalues of matrices, solving systems of linear differential
equations, etc.
3. CLOSEDMETHODS 4. BISECTION METHOD
- DESCRIPTION OF THE METHOD
- The method is to divide several times by half the sub-intervals
[a, b], and in each step, find the half that contains p. To begin
suppose that a1 = a and b1 = b, and p1 is the midpoint of [a, b]
is: p1 = (a1 + b1). If f (p) = 0, then p = p1; if not so, then f
(p1) has the same sign as f (a1) of (b1). If f (p1) f (a1) have the
same sign, then p exists between (p1, b1), and we took a2 = p1 and
b2 = b1. If f (p1) f (a1) have opposite signs, then p exists in the
inte5rvalo (a1, p1) and take a1 and a2 = b2 = p1. then reapply the
process to the interval [a2, b2].
5. ADVANTAGES AND DISADVANTAGES
- You are guaranteed the convergence of the root lock.
- management has a very clear error.
- The convergence can be long.
- No account of the extreme values (dimensions) as
6. BISECTION METHOD
- Suppose that f is a continuous function defined on the
interval
- [a, b] with f (a) f (b) of different signs. According to the
intermediate value theorem, there exists a number p in (a, b) such
that f (p) = 0.
- If f(a)=0 --> f(a) is root .
- If f(b)=0 --> f(b) is root
7. EXAMPLE
- Applying the bisection method to the function f (x) = x-x-1 for
the values a = 1.3 b = 1.4 with a tolerance of