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In which of the following categories can we put Bisection method?

In which of the following categories can we put Bisection method? Correct Answer Bracket Solutions

Explanation:

Bracketing Methods:

  • All bracketing methods always converge, whereas open methods (may sometimes diverge).
  • We must start with an initial interval , where f(a) and f(b) have opposite signs.
  • Since the graph y = f(x) of a continuous function is unbroken, it will cross the abscissa at a zero x = 'a' that lies somewhere within the interval .
  • One of the ways to test a numerical method for solving the equation f(x) = 0 is to check its performance on a polynomial whose roots are known.

Bisection method:

Used to find the root for a function. Root of a function f(x) = a such that f(a)= 0

Property: if a function f(x) is continuous on the interval and sign of f(a) ≠ sign of f(b). There is a value c belongs to such that f(c) = 0, means c is a root in between

Note:

Bisection method cut the interval into 2 halves and check which half contains a root of the equation.

1) Suppose interval .

2) Cut interval in the middle to find m : m = (a + b)/2

3) sign of f(m) not matches with f(a), proceed the search in new interval.

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