Interpolazione ed approssimazione simultanea di un insieme di dati di funzione e derivate prima e seconda. Descrizione del programma midia.

The problem of the least square fitting with fixed constraints is here solved in the general case of mixed data, i.e. functions and/or derivatives up to the second order. Given a set of linearly independent functions, the coefficients, the error matrix and the variance of the linear combination at any given point are determined. The abscissa and function (or derivatives) values can be reduced in any interval and the metric is consequently transformed. Making use of a sub-matrices method, the decrease of the weighted sum of the square of the residual for fits with higher number of functions is proved. The MIDIA code, which applies the obtained formulae, has been written in FORTRAN language for the IBM-7094 computer. As independent functions the most common polynomials (monomials, Legendre, Hermite, Chebychev etc....) are used. The program fits successively higher degree polynomials to input data and at each step the weighted sum of the square of the residual is given, and the one which will occur at the next step is predicted. The tabulation gives the values of the linear combination, of its first and second derivatives and of their standard deviations at any mesh point. If the number of input data is too large for an unique interpolation, an automatic disposal for grouping them is provided. [ABSTRACT FROM AUTHOR]

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