When we interpolate a function f given only data points ie, Basic Computer Science

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When we interpolate a function f given only data points ie

1. When we interpolate a function f given only data points, i.e., we do not know f or its derivatives, how can we gauge the accuracy of our approximation?

2. What are Chebyshev points and why are they important?

3. Describe osculating interpolation. How is it different from the usual polynomial interpolation?

4. What is a Hermite cubic interpolant?

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