Holistic Numerical Methods Institute

committed to bringing numerical methods to undergraduates

Multiple Choice Test

Spline Interpolation

Q1. The following n data points, (x1, y1), (x2, y2),...,(xn, yn) are given.  For conducting quadratic spline interpolation the x-data needs to be
equally spaced
in ascending or descending order
integers
positive

Q2. In cubic spline interpolation,

the first derivatives of the splines are continuous at the interior data points

the second derivatives of the splines are continuous at the interior data points
the first and the second derivatives of the splines are continuous at the interior data points

the third derivatives of the splines are continuous at the interior data points

Q3. The following incomplete y vs. x data is given

 x 1 2 4 6 7 y 5 11 ???? ???? 32

The data is fit by quadratic spline interpolants given by

,

where a, b, c, and d, are constants.  The value of c is most nearly

-303.00
-144.50
-0.0000
14.000

Q4. The following incomplete y vs. x data is given.

 x 1 2 4 6 7 y 5 11 ???? ???? 32

The data is fit by quadratic spline interpolants given by

,

where a, b, c, d, e, f, and g are constants.  The value of df/dxat x=2.6 is most nearly

-144.50

-4.0000

3.6000
12.200

Q5. The following incomplete y vs. x data is given

 x 1 2 4 6 7 y 5 11 ???? ???? 32

The data is fit by quadratic spline interpolants given by

where a, b, c, d are constants.  What is the value of ?

23.50

25.67

25.75

28.00

Q6. A robot needs to follow a path that passes through six points as shown in the figure.  To find the shortest path that is also smooth you would recommend which of the following?

Pass a fifth order polynomial through the data.

Pass linear splines through the data
Pass quadratic splines through the data

Regress the data to a second order polynomial

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