Math 373
Department of Mathematics and Computer Science
South Dakota School of Mines and Technology
Math 373 Solutions for linear and nonlinear systems 4_Root_Finding
1. Use Newton’s Method to approximate the solution to the following equation with an initial guess of x=1.
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2. Use False Position Method to find the root for
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3. Use Gauss-Jordan elimination to solve the following linear system of equations. Please show all your steps.
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4. Use Newton’s Method to solve the following system of nonlinear equations
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State your function and the proper Jacobian.
a) Use an initial guess of x=1, y=1, and z=1. Compute five iterations of Newton’s Method and give your approximation after each iteration.
b) Use an initial guess of x=0, y=0, and z=0. Compute five iterations of Newton’s Method and give your approximations after each iteration.
c) From the approximations you found by part a) and part b) which one is more accurate? How could you determine this when looking only at the information from the Newton iterations?
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