+ = =

Evaluating Eq. (4.124) at P = 1225 yields h( 1225, 1100) = 1556.5 Btu/Ibm. The error in this result is Error = 1556.5 - 1556.0 =0.5 Btu/Ibm.

4.8.2. Direct Multivariate Polynomial Approximation Consider the bivariate function, z = f(x, y), and the set of tabular data presented in Table 4.10. The tabular data can be fit by a multivariate polynomial of the form

The number of data points must equal the number of coefficients in the polynomial. A linear bivariate polynomial in x and y is obtained by including the first four terms in Eq. (4.125). The resulting polynomial is exactly equivalent to successive univariate linear polynomial approximation if the same four data points are used. A quadratic bivariate polynomial in x and y is obtained by including the first eight terms in Eq. (4.125). The number of terms in the approximating polynomial increases rapidly as the degree of approximation increases. This leads to ill-conditioned systems of linear equations for determining the coefficients. Consequently, multivariate high-degree approximation must be used with caution.