Bisection - Bisection Method James Keesling 1 The...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Bisection Method James Keesling 1 The Intermediate Value Theorem The Bisection Method is a means of numerically approximating a solution to an equation. f ( x ) = 0 The fundamental mathematical principle underlying the Bisection Method is the In- termediate Value Theorem . Theorem 1.1. Let f : [ a,b ] [ a,b ] be a continuous function. Suppose that d is any value between f ( a ) and f ( b ) . Then there is a c , a < c < b , such that f ( c ) = d . In particular, the Intermediate Value Theorem implies that if f ( a ) f ( b ) < 0, then there is a point c , a < c < b such that f ( c ) = 0. Thus if we have a continuous function f on an interval [ a,b ] such that f ( a ) f ( b ) < 0, then f ( x ) = 0 has a solution in that interval. The Intermediate Value Theorem not only guarantees a solution to the equation, but it also provides a means of numerically approximating a solution to arbitrary accuracy....
View Full Document

Page1 / 3

Bisection - Bisection Method James Keesling 1 The...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online