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AST 4101/Phys 4041 Midterm Exam
Fall 2012
Due in class on Monday, October 22, 2012Important! Be sure to read these instructions carefully. *This is a take home exam with the
following rules: a) You
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How to fill out constructing a cubic spline
How to fill out constructing a cubic spline
01
To fill out constructing a cubic spline:
02
Collect the data points for which you want to construct the cubic spline.
03
Sort the data points in ascending order based on the x-values.
04
Calculate the differences between adjacent x-values to find h[i] = x[i+1] - x[i].
05
Calculate differences between adjacent y-values to find delta[i] = (y[i+1] - y[i]) / h[i].
06
Set up a tridiagonal matrix A of size (n-2) x (n-2) where n is the number of data points.
07
Calculate the elements of the matrix A by using h[i] and delta[i] values.
08
Set up a coefficient matrix B of size (n-2) x 1.
09
Calculate the elements of the matrix B by using delta[i] values.
10
Solve the system of linear equations Ax = B to find the coefficients of the cubic spline.
11
Append the endpoints of the data points to the list of coefficients.
12
Plot the cubic spline using the calculated coefficients.
Who needs constructing a cubic spline?
01
Constructing a cubic spline is useful for anyone dealing with data that needs to be smoothed or interpolated.
02
It is commonly used in computer graphics for smooth curve interpolation.
03
Researchers, engineers, and scientists also use cubic splines in data analysis and modeling applications.
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