handout(4).pdf - Roots Bracketing Methods Azar Shakoori UOIT MATH 2070U Roots Bracketing Methods A very short introduction to errors Root-finding The

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Roots: Bracketing Methods Azar Shakoori UOIT MATH 2070U
Roots: Bracketing Methods A very short introduction to errors Root-finding The Intermediate Value Theorem The bisection method Examples Implementation details
Key questions I What are absolute error and relative error I What does the Intermediate Value Theorem mean? I What is meant by a bracket? I What is the bisection algorithm? I How does bisection work? I How can the bisection algorithm be implemented? What are meaningful convergence criteria for bisection?
Roots of a function: Root-finding Given function f , find x dom ( f ) such that f ( x ) = 0 I Roots, or zeros of nonlinear equations/functions I Classical terminology comes from square roots: x = 2 means x is a zero of f ( x ) = x 2 - 2 I Most equations have no closed form solution! I Iterative algorithms are needed to find solutions
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