= + + + = + +

Equation (4.142) can be verified by substituting the values in the table into the equations.

4.10 LEAST SQUARES APPROXIMATION Section 4.1 discusses the need for approximating functions for sets of discrete data (e.g., for interpolation, differentiation, and integration), the desirable properties of approximating functions, and the benefits of using polynomials for approximating functions. For small sets of smooth data, exact fits such as presented in Sections 4.3 to 4.9 are desirable. However, for large sets of data and sets of rough data, approximate fits are desirable. Approximate polynomial fits are the subject of this section.