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Obtain the third degree of langranges interpolating polynomial method ?
Barungi Regan
Mar 6
Obtain the third degree of langranges interpolating polynomial method ?
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Mar 6
To obtain the third degree of Lagrange's interpolating polynomial method, we need to have at least 4 data points. The third degree polynomial can be represented as:
P(x) = f(x0)*L0(x) + f(x1)*L1(x) + f(x2)*L2(x) + f(x3)*L3(x)
where L0(x), L1(x), L2(x), and L3(x) are the Lagrange basis polynomials of degree 3.
The Lagrange basis polynomials are given by:
L0(x) = (x-x1)(x-x2)(x-x3) / (x0-x1)(x0-x2)(x0-x3)
L1(x) = (x-x0)(x-x2)(x-x3) / (x1-x0)(x1-x2)(x1-x3)
L2(x) = (x-x0)(x-x1)(x-x3) / (x2-x0)(x2-x1)(x2-x3)
L3(x) = (x-x0)(x-x1)(x-x2) / (x3-x0)(x3-x1)(x3-x2)
By substituting the given data points (x0, f(x0)), (x1, f(x1)), (x2, f(x2)), and (x3, f(x3)) into the above equations, we can calculate the coefficients of the third degree Lagrange interpolating polynomial.
P(x) = f(x0)*L0(x) + f(x1)*L1(x) + f(x2)*L2(x) + f(x3)*L3(x)
where L0(x), L1(x), L2(x), and L3(x) are the Lagrange basis polynomials of degree 3.
The Lagrange basis polynomials are given by:
L0(x) = (x-x1)(x-x2)(x-x3) / (x0-x1)(x0-x2)(x0-x3)
L1(x) = (x-x0)(x-x2)(x-x3) / (x1-x0)(x1-x2)(x1-x3)
L2(x) = (x-x0)(x-x1)(x-x3) / (x2-x0)(x2-x1)(x2-x3)
L3(x) = (x-x0)(x-x1)(x-x2) / (x3-x0)(x3-x1)(x3-x2)
By substituting the given data points (x0, f(x0)), (x1, f(x1)), (x2, f(x2)), and (x3, f(x3)) into the above equations, we can calculate the coefficients of the third degree Lagrange interpolating polynomial.
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