What sort of error frustrates attempts to numerically, Basic Computer Science

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What sort of error frustrates attempts to numerically

1. What sort of error frustrates attempts to numerically differentiate a given smooth function to arbitrary accuracy? What is the step size h with smallest overall error?

2. Why is the numerical differentiation of noisy data a risky affair?

3. What is a differentiation matrix?

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Basic Computer Science: What sort of error frustrates attempts to numerically

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