Newton-Gregory Interpolation MCQs

Front

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

Back

n

Front

What is an interpolating polynomial?

Back

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

Front

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

Back

The degree of the interpolating polynomial.

Front

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

Back

Forward difference.

Front

Newton-Gregory forward interpolation is best suited for:

Back

Predicting values at the beginning of the data set.

Front

What is the purpose of Newton-Gregory interpolation?

Back

To estimate values of a function at points not explicitly given in the data set.

Front

What is a finite difference?

Back

A method for estimating the change in a function's value as its input changes.

Front

What is the formula for Newton's forward interpolation?

Back

P(x) = f(x_0) + (x-x_0)Δf(x_0) + (x-x_0)(x-x_1)Δ²f(x_0)/2! + ...

Front

What is the significance of the first divided difference?

Back

It represents the slope of the secant line between two data points.

Front

What is the relationship between interpolation and extrapolation?

Back

Interpolation estimates values within the range of data, while extrapolation estimates values outside that range.