lecture_14_rootfinding_6p

# lecture_14_rootfinding_6p - Lecture 10 root finding Main...

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1 General idea of root finding Matlab built in functions What does it mean to numerically solve for f(x)=0? The intermediate value theorem First root finding method: bisection Lecture 10: root finding Iterative implementation Recursive implementation Second root finding method: Newton Raphson Finding the minimum of a function Approximation by parabola The Newton Step Iterative implementation Recursive implementation Main problem in root finding Main problem: finding the root of an equation f(x) = 0, i.e. a point x where the function f is zero How to find the numerical value of this point? Matlab built in functions Matlab has a generic function called fzero which finds a zero of a function, based on a guess entered by a user. Declare function using function handle Call fzero, and specify guess Result is obviously π /2 in this case, as can be checked What questions are involved in solving g(x)=0? Root finding algorithms find numerical values such that the function g is “almost” zero, i.e. has small values. In this band, the function is “small enough” that it can be considered to be almost equal to zero What questions are involved in solving f(x)=0? Root finding algorithms find numerical values such that the function g is “almost” zero, i.e. has small values. What does this mean numerically? Let us zoom and see what is happening here. What questions are involved in solving f(x)=0? Root finding algorithms find numerical values such that the function g is “almost” zero, i.e. has small values. As long as the function is in the pink strip, we consider it equal to zero, thus any point in the corresponding horizontal segment is an approximation of the root

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2 What questions are involved in solving f(x)=0? This can be a problem if the function is too “flat”
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## This note was uploaded on 09/07/2011 for the course ENGIN 7 taught by Professor Horowitz during the Spring '08 term at Berkeley.

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lecture_14_rootfinding_6p - Lecture 10 root finding Main...

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