5. Below is a table of x and f(x) -2 10 21525 I f(x) 0 1511 1.2 2 Set up the equations for a 3rd order Cubic spline (aix³ + bix² + cix + di) To be able to solve the system of equations, two more pieces of information are required. Note, for as the order of the polynomial approximation is increased the number of constraints/boundary conditions increase. For quadratic spline we had on constraint, which for our in class example a5 = 0). For a cubic you will have two constraints, afor 4th order polynomial, you would have 4 constraints and so on. Using arbitrary constraints like setting the third derivative in the fourth point to zero may be used. However, the selection of a boundary condition, consisting of a pair of equations, is the commonly used method. The four conditions "natural spline", "not-a-knot spline", "periodic spline", and "quadratic spline".
5. Below is a table of x and f(x) -2 10 21525 I f(x) 0 1511 1.2 2 Set up the equations for a 3rd order Cubic spline (aix³ + bix² + cix + di) To be able to solve the system of equations, two more pieces of information are required. Note, for as the order of the polynomial approximation is increased the number of constraints/boundary conditions increase. For quadratic spline we had on constraint, which for our in class example a5 = 0). For a cubic you will have two constraints, afor 4th order polynomial, you would have 4 constraints and so on. Using arbitrary constraints like setting the third derivative in the fourth point to zero may be used. However, the selection of a boundary condition, consisting of a pair of equations, is the commonly used method. The four conditions "natural spline", "not-a-knot spline", "periodic spline", and "quadratic spline".
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5. Below is a table of x and f(x)
-2
10
21525
I
f(x)
0
1511
1.2
2
Set up the equations for a 3rd order Cubic spline (aix³ + bix² + cix + di)
To be able to solve the system of equations, two more pieces of information are required.
Note, for as the order of the polynomial approximation is increased the number of
constraints/boundary conditions increase. For quadratic spline we had on constraint,
which for our in class example a5 = 0). For a cubic you will have two constraints, afor 4th
order polynomial, you would have 4 constraints and so on. Using arbitrary constraints like
setting the third derivative in the fourth point to zero may be used. However, the selection
of a boundary condition, consisting of a pair of equations, is the commonly used method.
The four conditions "natural spline", "not-a-knot spline", "periodic spline", and "quadratic
spline".
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