(Solved): The Gregory Newton Forward Interpolation method is used to interpolate between equally spaced points ...

The Gregory Newton Forward Interpolation method is used to interpolate between equally spaced points using backward and forward differences. Problem Statement: During the night and early morning, the body temperature of a hospital patient rose dramatically, for an as-yet-unknown reason, until the nurse detected this variation and administered medication. You need to interpret this change in temperature. The body temperature was recorded at one-hour intervals as shown in the table. Exercise: Write a general MATLAB function for n th -order one-dimensional interpolation by the Gregory-Newton forward interpolation formula to solve this problem. Your code must check for the following: • Number of base points given must be at least n+1, otherwise change order and continue • Vectors of coordinates of base points must be the same size • Independent variable must be equally spaced (monotonic) • The vector of independent variables at which interpolation is required may be obtained using the MATLAB function linspace between 1 and 12. The function divides a range of time into 100 equally spaced points. Question: Using an order = 3, when did the patient’s temperature reach a maximum and what was the value of this temperature? If you change the order to 5, how does that affect your answers? Graph your results showing the experimental values with symbols and your interpolated values using a smooth curve. Introduction: The Gregory Newton Forward Interpolation method is used to interpolate between equally spaced points using backward and forward differences. Problem Statement: During the night and early morning, the body temperature of a hospital patient rose dramatically, for an as-yet-unknown reason, until the nurse detected this variation and administered medication. You need to interpret this change in temperature. The body temperature was recorded at one-hour intervals as shown in the table. Exercise: Write a general MATLAB function for \( n^{t h} \)-order one-dimensional interpolation by the Gregory-Newton forward interpolation formula to solve this problem. Your code must check for the following: - Number of base points given must be at least \( n+1 \), otherwise change order and continue - Vectors of coordinates of base points must be the same size Independent variable must be equally spaced (monotonic) - The vector of independent variables at which interpolation is required may be obtained using the MATLAB function linspace between 1 and 12. The function divides a range of time into 100 equally spaced points. Question: Using an order \( =3 \), when did the patient's temperature reach a maximum and what was the value of this temperature? If you change the order to 5 , how does that affect your answers? Graph your results showing the experimental values with symbols and your interpolated values using a smooth curve.