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第三问.txt

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+1.Both are polynomial interpolation methods, but their construction methods are different. Lagrange interpolation directly constructs interpolation polynomials, while Newton interpolation simplifies calculations through difference tables.
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+2.Without specific data, we cannot directly compare the numerical results of the two. But in general, if there are enough data points and their distribution is reasonable, the approximation effect of the two near the interpolation points should be similar. There is not much difference between the two answers to this question
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+3.The advantage of Newton interpolation is that if a new data point is added, only one row needs to be added to the difference table, without the need to recalculate the entire interpolation polynomial. Lagrangian interpolation requires recalculating all basis functions.