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**Unformatted text preview: **Lagrange interpolating Polynomials James Keesling 1 Determining the Coefficients of the Lagrange Interpolat- ing Polynomial by Linear Equations It is frequently the case that we will have certain data points, { ( x ,y ) , ( x 1 ,y 1 ) ,..., ( x n ,y n ) } , and will want to fit a curve through these points. In this chapter we will fit a polynomial of minimal degree through the points. We assume that the points { x ,x 1 ,...,x n } are all distinct. In that case we can fit a polynomial of degree n (or possibly less) through the points. If we write the polynomial in the following form, then we can use the points to determine the coefficients. L ( x ) = a + a 1 x + a 2 x 2 + + a n x n y = a + a 1 x + a 2 x 2 + a n x n y 1 = a + a 1 x 1 + a 2 x 2 1 + a n x n 1 . . . y n = a + a 1 x n + a 2 x 2 n + a n x n n We can solve these equations using matrices. The vector A = a a 1 ....

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