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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".

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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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".
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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