1.2 Bracketing Methods for Locating a root
1.2 Bracketing Methods for Locating a Root
Definition 1.3 (Root of an Equation, Zero of a Function. Assume that f(c) is a continuous function. Any number r for which f(r)=0 is called a root of the equation f(a)=0. Also, we say r is a zero of the function f(a)
1.2 1 The bisection method of bolzano
1.2.1 The Bisection Method of Bolzano
If f(a) and f(c have opposite signs, a zero lies in [a, c If f(c) and f(b) have opposite signs, a zero lies in c, bl If f(c=0, then the zero is c
Theorem 1.4(Bisection Theorem). Assume that f E Cla, b and that there exists a number r E [a, b such that f(r)=0. If f(a) and f(b) have opposite signs, and icn ingo represents the sequence of midpoints generated by the bisection process of (122)and(1.23),then r-cn|≤ (1.24) and there fore the sequence icn_o converges to the zero =r; that is m Cn=7 (1.25)