A third-order polynomial of the form y = Ax^3 + Bx^2 + Cx + D is to be fitted to

Question

A third-order polynomial of the form y = Ax^3 + Bx^2 + Cx + D is to be fitted to four time-velocity data points. At time x = 0, 1, 2, and 3 s, the velocity is measured as 7, 14, 29, and 58 m/s. Using Gauss-Jordan elimination, find the curve that passes through these points. Also, solve the problem by employing the backslash operator in MATLAB and compare the results with those obtained earlier. Problem 6.5 Use partial pivoting Compare with matlabrref or inv (or other program language equivalent) or TI calculator rref Problem 6 12 Problem 6 16 Use Gauss Elimination Use Gauss-Jordan Elimination Use Inverse Method Compare with matlabrref or inv (or other program language equivalent) or TI calculator rref Problems 6.5, 6 12, 6 16 due 7/10/17 Problem 6.24 Use Gauss-Seidel iteration Use Jacobi iteration Compare with matlabrref or inv (or other program language equivalent) or TI calculator rref

Explanation / Answer

y = Ax^3 +B*x^2 + c*x + D

7 = D

14 = A+ B + C +D

29 = 8A+4B+2C+D

58 = 27A+9B+3C+D

Matlab: -

A = [27 9 3 1 ; 8 4 2 1 ; 1 1 1 1 ; 0 0 0 1];
>> b =[58 ;29 ; 14 ;7];
>> A

ans =

1.0000
1.0000
5.0000
7.0000

y = x^3 + x^2 + 5x + 7

by gauss-jordan ,same result comes

Solution set:

x1 = 1

x2 = 1

x3 = 5

x4 = 7

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