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3 cards from this section. Quick, good the night before a test.
What is zero-stability?
Think about how errors affect numerical solutions.
Why is the characteristic equation important?
Consider what the roots indicate for stability.
What is zero-stability?
Focus on the relationship between errors and solution accuracy.
True or False: For zero-stability, roots of the characteristic equation can lie outside the unit circle.
Think about how this affects solution growth.
Given the characteristic polynomial z^3 - 1 = 0, assess the zero-stability of the corresponding method.
Graph the roots on the complex plane to visualize their location.
Consider the characteristic equation z^3 - 2z^2 + z - 1 = 0. Are these roots zero-stable? Provide your reasoning.
Use the quadratic formula if necessary and evaluate each solution.
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