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hw8 - dx=10 6 Use it to find a root of the equation x 3 sin...

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Physics 503: Scientific Computing Homework #8 Topic: Roots finding and systems of equations Due: Thurs. 4/13 by the beginning of class - DON’T forget to include output and plot printouts! (please email your code to [email protected] ) Assignment 1. Finish your ‘brute force’ function to find the root of an equation. Refine it so that once a root is passed, the step size is reduced by ½ and repeat over the smaller interval. You could even think of how to do this recursively until the root is bracketed by some minimum interval (like
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Unformatted text preview: dx=10 6 ). Use it to find a root of the equation x 3 sin( x ) − 1 between x=[0,3]. 2. Compare your results with the bisection and Newton-Raphson methods we discussed in class. Add some timing routines to compare the different methods. 3. Use the ‘matrix’ object in numpy and solve function in scipy.linalg to solve the following systems of algebraic equations: 3 x + 8 z = 3 − 2 x + 6 y − 2 z = 1 0.5 y + 2 z = 9...
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