vandemonde.pdf
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28 Interpolation using the Vandermonde matrix The most basic procedure to determine the coefficients a0 , a1 , . . . , an of a polynomial Pn (x) = a0 + a1 x + a2 x2 + · · · + an xn such that it interpolates the n + 1 points (x0 , y0 ), (x1 , y1 ), . . . , (xn , yn ) is to write a linear system of equations as follows: Pn (x0 ) = y0 ⇒ ao + a1 x0 + a2 x20 + · · · + an−1 x0n−1 + an xn0 = y0 Pn (x1 ) = y1 ⇒ ao + a1 x1 + a2 x21 + · · · + an−1 x1n−1 + an xn1 = y1 .. . .…
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