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Lecture16Summary

# Lecture16Summary - E7 Intro to Computer Lectures 16&17 Root...

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E7: Intro to Computer. . . Lectures 16&17: Root Finding Tad Patzek, Civil & Environmental Engineering, U.C. Berkeley March 31, 2008

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. . . Announcements. . . For this week read: Class Notes E7Lectures 16&17 Class Book Chapra II, Roots and Optimization Prof. T.W. Patzek’s E7 Lecture 16: . . . – p.1/25
. . . Today’s and Next Lectures. . . We will learn about Roots of nonlinear functions Function handles The bisection method The Newton’s method Prof. T.W. Patzek’s E7 Lecture 16: . . . – p.2/25

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Files to download. . . showbisection.m demonstrates how the bisection method works. shownewton.m demonstrates how Newton’s method works. funcd.m is a cubic polynomial used by the showbisection and shownewton demos. rootbisection.m finds a previously bracketed root of a function using the bisection method; based on the Numerical Recipes in C . rootnewton.m using a close enough guess for a root, find the root using Newton’s method; based on the Numerical Recipes in C . Prof. T.W. Patzek’s E7 Lecture 16: . . . – p.3/25
Files to download. . . rootsafe.m in an interval [ x 1 , x 2 ] containing a root, find the root using a combination of bisection and Newton’s method; based on the Numerical Recipes in C . PlotZCubed Plots the three complex roots of z 3 1 . domains.m plots the naïve domains of attraction of all three roots of f ( z ) = z 3 1 , where z is the complex variable. truedomains.m finds the complex roots of f ( z ) = z 3 1 for a very fine grid of initial guesses on an ( x, y ) -square between -1 and 1 (a unit square on the complex plane), thus generating the beautiful Julia fractal for the true domains of influence of each root.

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• Spring '08
• Patzek
• Numerical Analysis, Complex number, Root-finding algorithm, Prof. T.W. Patzek

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