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-2 1 5 10 15 4. Given the data points (0, 1), (1, 2), (2, 0) and (3,2), construct the quadratic spline interpolation formula as we did class, and using the same constraining boundary condition 5. Below is a table of x and f(x) x f(x) 0 5 1 1.2 2 Set up the equations for a 3rd order Cubic spline (a₁x³ + bx² + c¡x + 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".

-2 1 5 10 15 4. Given the data points (0, 1), (1, 2), (2, 0) and (3,2), construct the quadratic spline interpolation formula as we did class, and using the same constraining boundary condition 5. Below is a table of x and f(x) x f(x) 0 5 1 1.2 2 Set up the equations for a 3rd order Cubic spline (a₁x³ + bx² + c¡x + 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
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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-2 1 5 10 15 4. Given the data points (0, 1), (1, 2), (2, 0) and (3,2), construct the quadratic spline interpolation formula as we did class, and using the same constraining boundary condition 5. Below is a table of x and f(x) x f(x) 0 5 1 1.2 2 Set up the equations for a 3rd order Cubic spline (a₁x³ + bx² + c¡x + 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:-2 1 5 10 15 4. Given the data points (0, 1), (1, 2), (2, 0) and (3,2), construct the quadratic spline interpolation formula as we did class, and using the same constraining boundary condition 5. Below is a table of x and f(x) x f(x) 0 5 1 1.2 2 Set up the equations for a 3rd order Cubic spline (a₁x³ + bx² + c¡x + 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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