Which numerical application uses a Vandermonde matrix to determine the coefficients of a polynomial passing through a given set of data points?
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Polynomial interpolation
A Vandermonde matrix represents a system of linear equations where each row contains the powers of a specific data point's x-coordinate. While this method guarantees a unique polynomial that passes through every point, the matrix becomes notoriously 'ill-conditioned' as more points are added, often leading to significant numerical errors.
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- Which numerical task involves finding a degree n-1 polynomial through n points using a Vandermonde matrix?