Find the linear spline which interpolates the data Compare i

Find the linear spline which interpolates the data Compare interpolated values at x=2.5 and x=5.5 to f(x) = squareroot x -1

Solution

(a).((X-1)(X - 10)(X - 17))/120-((X/3 - 1/3)*(X - 5)*(X - 17))/105 +((X/16 - 1/16)(X - 5)*(X - 10))/21;

F(X)= ((X - 1)*(3X² - 101X + 1270))/1680;

Verification:

F(5)=((5 - 1)*(3*25 - 101*5 + 1270))/1680=2

F(1)=0;

(b)f(2.5)= 1.2247

    F(5.5)= 2.1213