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Is this true?

Increasing the number of equally spaced interpolation nodes improves the approximation

No — it is false.

The counterexample

Runge's function on [−1, 1]

The interpolants diverge near the endpoints as . Chebyshev nodes restore convergence.

The kind of mistake this is

Execution slip

The idea was right. The computation was not.

Drill statements like this
numerical

Others that fail the same way

From Numerical Analysis › Interpolation and numerical integration with error terms

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