Calc Num Prato 01(21.05.09)

The document discusses approximation of functions and data through interpolation. It introduces polynomial interpolation as a common method of approximating functions where only some function values are known. The key points covered are: - Polynomial interpolation finds a polynomial that passes exactly through a set of known data points. Higher degree polynomials can fit more points. - The Vandermonde matrix and method of indeterminate coefficients are methods for calculating the polynomial coefficients to exactly interpolate the given data points. - Polynomial interpolation provides a simple model for the data but the Vandermonde matrix becomes ill-conditioned as the number of points increases, requiring alternative methods. - Lagrangian polynomials provide an alternative basis for representing interpolating polynomials that can be numerically