The gamma function is defined by It is known that for integer numbers the function has the value (We

The gamma
function is defined by

It is known
that for integer numbers the function has the value

(We define
0! = 1.) Thus, for example, (1,1),(2,1),(3,2),(4,6),(5,24) can be used as data
points for an interpolating polynomial.

(a) Write a
MATLAB script that computes the polynomial interpolant of degree four that passes
through the above five data points.

(b) Write a
program that computes a cubic spline to interpolate the same data. (You may use
MATLAB’s sp line.)

(c) Plot the
two interpolants you found on the same graph, along with a plot of the gamma function
itself, which can
»

The gamma
function is defined by

It is known
that for integer numbers the function has the value

(We define
0! = 1.) Thus, for example, (1,1),(2,1),(3,2),(4,6),(5,24) can be used as data
points for an interpolating polynomial.

(a) Write a
MATLAB script that computes the polynomial interpolant of degree four that passes
through the above five data points.

(b) Write a
program that computes a cubic spline to interpolate the same data. (You may use
MATLAB’s sp line.)

(c) Plot the
two interpolants you found on the same graph, along with a plot of the gamma function
itself, which can be produced using the MATLAB command gamma.

(d) Plot the
errors in the two interpolants on the same graph. What are your observations?

»

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