Interpolation

In Newton's forward interpolation, what is the significance of the forward differences?

• They represent the slopes of the interpolating polynomial at the data points.

• They represent the coefficients of the interpolating polynomial.

• They represent the errors between the interpolating polynomial and the actual function.

• They represent the distances between the data points.

What is the primary purpose of using Newton's backward interpolation method?

• To estimate values of a function at points not in the dataset.

• To find the derivative of the interpolating polynomial.

• To minimize the error in polynomial approximation.

• To calculate the area under the curve of the function.

In the context of interpolation, what role do divided differences play?

• They provide a way to compute the coefficients of the interpolating polynomial.

• They help in determining the convergence of the interpolation method.

• They are used to measure the smoothness of the function being interpolated.

• They indicate the number of data points required for interpolation.

How does the choice of interpolation method affect the accuracy of the results?

• Different methods have varying degrees of sensitivity to data point placement.

• All methods yield the same accuracy regardless of the data points.

• Interpolation methods do not affect accuracy; only the number of data points does.

• More complex methods always provide more accurate results.

Stirling's interpolation formula is mainly used for:

• Unequally spaced data points

• Equally spaced data points

• Extrapolation

• Solving ordinary differential equations

Which interpolation method is generally more suitable for interpolating data near the end of a given interval?

• Newton's forward interpolation

• Newton's backward interpolation

• Both methods are equally suitable

• Neither method is suitable

Bessel's interpolation formula is a modification of which interpolation method?

• Lagrange interpolation

• Newton's divided difference interpolation

• Hermite interpolation

• Cubic spline interpolation

Which interpolation method is generally considered more accurate for interpolating data with a large number of points?

• Lagrange interpolation

• Newton's divided difference interpolation

• Bessel's interpolation

• Gauss's interpolation

Gauss's interpolation formula is particularly useful for interpolating data near which points?

• The beginning of the data interval

• The end of the data interval

• The middle of the data interval

• All of the above

Find x if x0 = 0.6, n = 2.6 and h = 0.2

• 12

• 1.2

• 1.22

• 1.12