I want a function that passes through the (x,y) points (3,0),(4,-1),(6,3) and (7,2). Using Lagrange

Sahar Bowden

Sahar Bowden

Answered question

2022-02-17

I want a function that passes through the (x,y) points (3,0),(4,-1),(6,3) and (7,2). Using Lagrange interpolation I get
x315x2+70x1022 but using this interpolation method for rational functions I get the much simpler (x3)(x5). This is a case where the rational function interpolation is a lot simpler than polynomial interpolation.
Is there a method to get (x3)(x5) given the points above, a sort of interpolation method that uses rational functions?

Answer & Explanation

Kathleen Mcpherson

Kathleen Mcpherson

Beginner2022-02-18Added 9 answers

f(x)=x315x2+70x1022
g(x)=x3x5
pass through points (3,0),(4,-1),(6,3),(7,2).
But what does happen if you want to interpolate close to x=5?f(5)=1 but g(5±)=±. This makes a small problem, isn't ?

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