(BQ) Part 2 book "Applied numerical methods" has contents: Linear regression, fourier analysis, polynomial interpolation, splines and piecewise interpolation, numerical integration formulas, numerical integration of functions, numerical differentiation, boundary value problems,.and other contents. | Part Four Curve Fitting OVERVIEW What Is Curve Fitting? Data are often given for discrete values along a continuum. However, you may require estimates at points between the discrete values. Chapters 14 through 18 describe techniques to fit curves to such data to obtain intermediate estimates. In addition, you may require a simplified version of a complicated function. One way to do this is to compute values of the function at a number of discrete values along the range of interest. Then, a simpler function may be derived to fit these values. Both of these applications are known as curve fitting. There are two general approaches for curve fitting that are distinguished from each other on the basis of the amount of error associated with the data. First, where the data e xhibit a significant degree of error or “scatter,” the strategy is to derive a single curve that represents the general trend of the data. Because any individual data point may be incorrect, we make no ffort to intersect every point. Rather, the curve is designed to follow the e pattern of the points taken as a group. One approach of this nature is called least-squares regression (Fig. ). Second, where the data are known to be very precise, the basic approach is to fit a curve or a series of curves that pass directly through each of the points. Such data usually originate from tables. Examples are values for the density of water or for the heat capacity of gases as a function of temperature. The estimation of values between well-known discrete points is called interpolation (Fig. and c). Curve Fitting and Engineering and Science. Your first exposure to curve fitting may have been to determine intermediate values from tabulated data—for nstance, from interest tai bles for ngineering eco omics or from steam e n tables for thermodynamics. Throughout the remainder of your career, you will have frequent o ccasion to estimate intermediate values from such tables. Although .
