Holistic Numerical Methods

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MULTIPLE CHOICE TEST

(All Tests)

SPLINE INTERPOLATION

(More on Spline Interpolation)

INTERPOLATION

(More on Interpolation)


Pick the most appropriate answer.


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/dx at 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

 

 


 

 

Complete Solution

 

Multiple choice questions on other topics

 


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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

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