Newton-Gregory Interpolation - MCQs

What is an interpolating polynomial?

• A polynomial that exactly fits a set of given data points

• A polynomial that approximates a function but does not necessarily pass through data points

• A polynomial used only for numerical differentiation

• A polynomial that is always of degree one

The degree of an interpolating polynomial passing through n+ 1 data points is at most:

• n

• n+ 1

• 2n

• n−1

In Newton-Gregory forward interpolation, which finite difference is used?

• Backward difference

• Central difference

• Forward difference

• Mixed difference

What is the main disadvantage of high-degree polynomial interpolation?

• It is computationally expensive

• It leads to oscillations (Runge’s phenomenon)

• It requires equally spaced data

• It works only for linear functions

The Newton-Gregory backward interpolation formula is expressed in terms of:

• Forward differences

• Backward differences

• Central differences

• Divided differences

The order of accuracy of Newton-Gregory interpolation depends on:

• The step size

• The degree of the interpolating polynomial

• The first derivative of the function

• The method of numerical differentiation

In Newton-Gregory forward interpolation, the interpolating polynomial is expressed in terms of:

• Forward differences and step size

• Backward differences and step size

• Divided differences and variable step size

• Taylor series expansion

Newton-Gregory interpolation formulas are valid when the values of x are:

• Unequally spaced

• Equally spaced

• Logarithmically spaced

• Randomly spaced

If the interpolation point is closer to the last tabulated value, which interpolation should be used?

• Newton-Gregory forward interpolation

• Newton-Gregory backward interpolation

• Lagrange interpolation

• Newton-Raphson method

Newton-Gregory forward interpolation is best suited for:

• Predicting values at the beginning of the data set

• Predicting values at the end of the data set

• Solving nonlinear equations

• Integrating a function